Bachelor of Technology Sudip Roy Dr. Partha Pratim Chakrabarti

Qualitative Reasoning :Modeling and Reasoning

aboutIncomplete Qualiative Temporal Information

Thesis submitted in partial fulfillment

of the requirements for the degree

of

Bachelor of Technology

by

Sudip Roy

under the guidance of

Dr. Partha Pratim Chakrabarti

Department of Computer Science and EngineeringIndian Institute of Technology Kharagpur

Kharagpur, WB 721302, IndiaMay 2009

Qualitative Reasoning :Modeling and Reasoning

aboutIncomplete Qualiative Temporal Information

Thesis submitted in partial fulfillment

of the requirements for the degree

of

Bachelor of Technology

by

Sudip Roy

under the guidance of



Kharagpur, WB 721302, IndiaMay 2009


Kharagpur, 721302, India.

Certificate

This is to certify that the thesis entitled Qualitative Temporal Reasoning: Modeling andReasoning about Incomplete Qualitative Temporal Information, submitted by SudipRoy, Undergraduate Student, in the Department of Computer Science and Engineering, In-

dian Institute of Technology, Kharagpur, India, for the award of the degree of Bachelor ofTechnology, is a record of an original research work carried out by him under my supervi-

sion and guidance. The thesis fulfills all requirements as per the regulations of this Institute.

Neither this thesis nor any part of it has been submitted for any degree or academic award

elsewhere.


Acknowledgments

I owe my deepest gratitude to my supervisor, Dr. Partha Pratim Chakrabarti for the

free exchange of ideas, constructive criticism, guidance, encouragement and moral support

throughout the work. It is his supervision with the clear ideas and sharp mind that helped

me to be focused in the right direction. Without his invaluable advice and support it would

not have been possible to complete this work.

I would also like to express my gratitude to Mr. Subrat Panda (Research Scholar) whose

constant encouragement and motivation helped me in completing this work.

I would like to thank my parents for their support and encouragement. It is their prayers

and best wishes that I could complete this mammoth task.

Sudip Roy

AbstractIn this work, we propose a novel formal model which can conveniently model a com-

plex environment with large numbers of states in a simple and concise manner. We model a

dynamic system in terms of objects which are passive entities possessing certain qualitative

properties and processes which capture the change in these properties. The model is based

on qualitative calculus which allows a flexible representation of only the information that is

available and actually needed. It is targeted towards representation of physical phenomena

taught at school and college levels, so as to act as an aid for teaching and understanding

of the basics of physics.

Previous published related works in the field build models to capture a single qualitative

state without any form of temporal ordering of processes. We use the timegraph data struc-

ture to capture the temporal relation between the processes. We also propose algorithms

for state space exploration and address the problem of reachability of a qualitative state.

As part of this work, a software has been developed as an interface for designing mod-

els and reasoning using them. The software provides for a user friendly drawing interface

for creation and specification of the model. The visual representation is translated into a

XML based language, QML which is parsed to build the models. The software simulates

the model using the algorithms mentioned above. In order to promote its functionality as a

teaching aid, we generate easy to understand explanations of the model and its behaviour

in natural language. The explanation is given at two levels : an overview of the model

and an indepth analysis which explains each state, path and cycle in the state transition

diagram.

Contents

1 Introduction 11.1 Motivation and Aim of the Work . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Introduction To Qualitative Reasoning . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.2 Qualitative Representations . . . . . . . . . . . . . . . . . . . . . 2

1.2.3 State, Time and Behaviours . . . . . . . . . . . . . . . . . . . . . 3

1.2.4 Qualitative State Graph . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Discussion on Problems Addressed . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Outline of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Study of Related Topics 52.1 Temporal Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Linear-Time Temporal Logic . . . . . . . . . . . . . . . . . . . . . 5

2.1.2 Branching-Time Temporal Logic (Computation Tree Logic) . . . . 6

2.2 Qualitative Reasoning over Time . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Interval and Point Algebra . . . . . . . . . . . . . . . . . . . . . . 6

2.2.2 TL-Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.3 Timegraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 VModel - A Single State Qualitative Model . . . . . . . . . . . . . . . . . 9

2.3.1 Vmodel Ontology . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.2 VModel Advantages and Limitations . . . . . . . . . . . . . . . . 10

2.3.3 Extensions to VModel . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Qualitative Temporal Model 133.1 Entity-Relationship-Process Model . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 Model Ontology . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Formal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

ii CONTENTS

3.2.1 Entity Specification . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.2 Process Specification . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.3 Temporal Graph Specification . . . . . . . . . . . . . . . . . . . . 15

3.2.4 Qualitative State . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3 Grammar for Model Specification . . . . . . . . . . . . . . . . . . . . . . 16

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Reasoning Algorithms 194.1 State Space Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.2 Cycle Detection in Qualitative State Transition Diagram . . . . . . . . . . 21

4.3 Reachability Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.3.1 Transitive Closure Computation . . . . . . . . . . . . . . . . . . . 22

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5 QualSym : Implementation and Software Development 235.1 Visual Drawing Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.2 QML - Qualitative Modeling Language . . . . . . . . . . . . . . . . . . . 23

5.2.1 Parsing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.2.2 Visual Model to QML . . . . . . . . . . . . . . . . . . . . . . . . 25

5.2.3 QML to Visual Model . . . . . . . . . . . . . . . . . . . . . . . . 25

5.3 Natural Language Generation . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.4 Querying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

6 Conclusions and Recommendations for Further Work 276.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

6.2 Extension beyond Point Algebra . . . . . . . . . . . . . . . . . . . . . . . 27

6.3 Compositionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6.4 Information Extraction from Textual Explanations . . . . . . . . . . . . . . 28

A Examples 29A.1 Oscillations of a Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . 29

A.1.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . 29

A.1.2 Visual Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

A.1.3 QML Specification . . . . . . . . . . . . . . . . . . . . . . . . . . 29

A.1.4 State Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

A.1.5 Qualitative State Transition Diagram . . . . . . . . . . . . . . . . . 34

CONTENTS iii

A.1.6 Explanation in Natural Language . . . . . . . . . . . . . . . . . . 34

A.1.7 Testing Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . 37

A.2 Three Tank Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

A.2.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . 37

A.2.2 Visual Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

A.2.3 QML Specification . . . . . . . . . . . . . . . . . . . . . . . . . . 38

A.2.4 State Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.2.5 Qualitative State Transition Table . . . . . . . . . . . . . . . . . . 48

A.2.6 Explanation in Natural Language . . . . . . . . . . . . . . . . . . 54

A.2.7 Testing Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . 56

BIBLIOGRAPHY 58

List of Figures

2.1 Basic Relations of Allen’s Interval Algebra . . . . . . . . . . . . . . . . . 7

2.2 Example of a TL-graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5.1 Drawing Interface of QualSym . . . . . . . . . . . . . . . . . . . . . . . . 24

A.1 Pendulum System in QualSym . . . . . . . . . . . . . . . . . . . . . . . . 30

A.2 Three Tank System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

A.3 Qualitative Model for Three Tank System . . . . . . . . . . . . . . . . . . 38

Chapter 1

Introduction

1.1 Motivation and Aim of the Work

One of the primary purposes and motivations of qualitative reasoning is to emulate the

thought process of humans. Thus it is clear that reasoning and inferencing from qualita-

tive information is much more easier for humans. Consider for example “the car heading

towards us is slowing down” versus “the derivative of the car’s speed along the line con-

necting us is -12mph”. Clearly the first description of the event which is a qualitative one

is much more easily processed by a person than the second one in spite of the second one

containing more information than the first.

This project aims at developing a qualitative model which can capture the behavior of a

physical system and thus serve as a learning and teaching aid for students. We try to develop

sound and complete models which can capture the behaviour of a physical system. We

propose efficient algorithms to explore all possible qualitative states of the system and make

suitable inferences which serve us in understanding the physics behind the phenomena in

an intuitive manner. We also look into the reachability problem i.e. given a state of the

system, is another qualitative state reachable from the given state. In order to promote it as

an teaching aid, we provide natural language explanations of the model.

An analysis of the utility of the project can be best discussed with the following ex-

ample. Consider an example : What is the difference between classroom teaching and

reading from a book ? Firstly,teachers usually tend to explain the problem in a system-

atic way. They start by providing a top level explanation of the problem without directly

jumping into the equations or formulae. A top level qualitative explanation introduces

the problem to the students, and lays the foundation for an in depth quantitative analysis.

Secondly, the teacher differs from a book because of the fact that he/she can interpret the

2 Introduction

queries/questions of the students and can answer them suitably, modifying his/her answers

over subsequent queries. This is something which the book fails to do. Thus, if we can

create qualitative models which capture all possible behaviors of the system, then we can

not only reason but also answer specific queries and refine the system with each additional

information. Thirdly, the model serves as a compact representation of the entire problem.

(Cognitive Economy)

1.2 Introduction To Qualitative Reasoning

Qualitative reasoning is the area of AI which creates representations for continuous aspects

of the world, such as space, time and quantity, which support reasoning with very little

information.[5]

1.2.1 Motivation

Qualitative reasoning is motivated by two observations [3].

• People draw useful and subtle conclusions about the physical world without differ-

ential equations. In our daily lives we figure out what is happening around us and

how we can affect it, working with far less data, and less precise data, than would be

required to use traditional, purely quantitative methods

• Scientists and Engineers appear to use qualitative reasoning when initially under-

standing a problem, when setting up more formal methods to solve particular prob-

lems, and when interpreting the results of qualitative simulations, calculations, or

measurements.

.

1.2.2 Qualitative Representations

Qualitative representations provide notations for describing and reasoning about continu-

ous properties of the physical world. While hybrid models discretize the continuous do-

main in order to reason about the system, the knowledge in the hybrid models is complete.

Qualitative models on the other hand reason about incomplete knowledge by providing an

abstraction of the knowledge. [9, 15] Two key issues in qualitative representations are res-

olution and compositionality. [8]

Resolution : Resolution concerns the level of information detail in a representations. Res-

olution is an issue because the goal of qualitative reasoning is to understand how little

1.3 Discussion on Problems Addressed 3

information suffices to draw useful conclusions. Low resolution information is available

more often than precise information.

Compositionality : Compositionality concerns the ability to combine representations for

different aspects of a phenomenon or system to create a representation of the phenomenon

or system as a whole. It is an issue because one goal of Qualitative Reasoning is to formal-

ize the modeling process itself.

1.2.3 State, Time and Behaviours

A qualitative state is a set of propositions that characterize a qualitatively distinct behavior

of a system. A qualitative state describing a falling ball, for instance, would include infor-

mation about what physical processes are occurring (e.g. motion downwards, acceleration

due to gravity) and how the parameters of the ball change (e.g. its position is getting lower

and its downward velocity is increasing).

Qualitative representations can be used to partition behavior into natural units. Quali-

tative state can have transitions to several next states, reflecting ambiguity in the qualitative

representations.

A sequence of qualitative states occurring over a particular span of time is called be-

havior. Behaviors can be described using purely qualitative knowledge, purely quantitative

knowledge, or a mixture of both.

1.2.4 Qualitative State Graph

A Qualitative State Graphis a graphical representation of the qualitative model of the sys-

tem in which each node corresponds to a distinct qualitative state and each transition be-

tween these states correspond to edges in the state graph. The behaviors of a system is a

sequence of qualitative states occurring over a particular span of time [11].

If continuous values are represented by quantity spaces and sources of comparisons are

limit points, then a finite set of qualitative states is sufficient to describe every possible

behaviours of the system. A collection of such qualitative states and their transitions is

called envisionment.

1.3 Discussion on Problems Addressed

In this work, we address the problem of generating the Qualitative State Graph from a

model. We model every physical system as a collection of passive entities and a system

4 Introduction

of interacting processes which change the properties of the entities and hence define their

behaviour in the environment.

Given a model, we use qualitative reasoning techniques to generate the qualitative state

graph which captures every possible qualitative state the system can be and also provides

us information on the various paths along which the state can be reached. The model allows

for a polynomial representation of an exponential number of states of the system and thus

is extremely concise. The task of computing the qualitative state graph from the model is

at an abstract level similar to the problem of constructing a Deterministic Finite Automata

from a Non-Deterministic one, but with qualitative calculus involved.

Since, the work is directed towards facilitating understanding of school level physics,

it is important to provide for easy representation of the information. We achieve it in two

ways -

• visual drawing interface to specify the model.

• generating natural language explanations of the phenomena to aid understanding

1.4 Outline of Thesis

In chapter 2 we introduce the fundamentals necessary for understanding and appreciating

the work. These include basics of temporal logic, qualitative representations, time graphs,

efficient algorithms for reasoning over time and a small discussion on VModel which at-

tempts to solve a similar problem. After establishing the motivation and learning the fun-

damentals, in chapter 3 we propose out formal model and define the syntax and semantics

of the model. We also provide a grammar for generating a specification of the model. In

chapter 4, we discuss algorithms for solving the various problems associated with reason-

ing. The implementation and software development aspects of the project are discussed

briefly in chapter 5. This includes a discussion on the generation of natural language expla-

nation for the model. We conclude in chapter 6 and provide recommendations for further

directions of research on the topic. We discuss in detail the complete workflow on two

commonly referred to problems in the field - the oscillations of a pendulum and the three

tank problem.

Chapter 2

Study of Related Topics

2.1 Temporal Logic

Temporal logic is a convenient formalism for specifying and verifying properties of reactive

systems, as first pointed out by Pnueli in 1977. A formula of temporal logic describes the

set of infinite sequences for which it is true, also known as a temporal property . A given

system satisfies a property if all of its computations belong to this set. [10]

2.1.1 Linear-Time Temporal Logic

A model of linear-time temporal logic (LTL) is an infinite sequence of states where each

point in time has a unique successor. Temporal formulas are evaluated over such a sequence

of states together with an index i=0,1,2,... of the i’th state.

Syntax and Informal Description

Besides the usual logical connectives, temporal formulas can be composed using temporaloperators. We describe these briefly, with p and q being sub-formulas.

Future Temporal Operators

[]p Henceforth p

<>p Eventually p

p Until q q holds some time in the future, and p holds at

least up to the first q

p Awaits q Either p holds indefinitely, or p Until q

()p p holds at the next time instance

Past Temporal Operators

6 Study of Related Topics

[-]p So-far p

<->p Once p

p Since q q did hold some time in the past, and p held at least

down to the first q

p Backto q Either p Since q, or [-]p

(-)p p holds at the previous time instance (and

current time is not 0)

(˜)p p holds at the previous time instance or the

current time is 0 (there is no previous time instance)

Semantics

A temporal logic formula p is satisfiable if there is a sequence of states S such that S,0

|= p. It is valid if the negation is unsatisfiable. A propositional temporal formula is a

temporal formula where all atoms are propositional variables (a propositional temporal

formula therefore does not contain quantification and compound predicates).

2.1.2 Branching-Time Temporal Logic (Computation Tree Logic)

LTL implicitly quantifies universally over paths. Therefore, properties which assert the

existence of a path can be expressed in LTL. Branching-time logics solve this problem by

allowing us to quantify explicitly over paths.

Computation Tree Logic is a branching time logic, meaning that its model is a tree-like

structure in which the future is not determind; there are different paths in the future, any

one of which might be the ’actual’ path that is realized.

2.2 Qualitative Reasoning over Time

In this section we analyze the various temporal representations and reasoning algorithms

proposed [18, 1, 13].

2.2.1 Interval and Point Algebra

Reasoning about temporal constraints is an important task in many areas of computer sci-

ence and elsewhere including scheduling, natural language processing, planning, database

theory, technical diagnosis, circuit design etc [17, 12, 19]. Among the frameworks for

formalizing this type of problem are:

• Point algebra (by van Beek and Cohen) - For expressing relations between time

points

2.2 Qualitative Reasoning over Time 7

• Point Interval Algebra (by Vilain) For expressing relations between time points and

intervals

• Allen’s Interval Algebra For expressing qualitative information between time inter-

vals

State space approaches provide a crude sense of time that is useful in simple problem-

solving tasks. A state is a description of the world (i.e., a database of facts) at an instanta-

neous point in time. Actions are modeled in such systems as functions mapping between

states.

Point Algebra (PA) uses points as the fundamental units and there are 3 possible prim-

itive relations (<,=, >) between any two points. Interval Algebra uses thirteen basic rela-

tions between intervals (shown in the figure below).

Figure 2.1: Basic Relations of Allen’s Interval Algebra


2.2.2 TL-Graphs

Timegraphs are graphs partitioned into a set of chains on which the search is supported by

a metagraph data structure. The algorithms herein enable construction of a timegraph from

a given set of PA-relations, querying a timegraph, and efficiently checking the consistency

of a timegraph augmented by a set of PA-disjunctions [7, 2].

Representing temporal relations through graphs

Definition 1 : A temporally labeled graph (TL-graph) is a graph with at least one vertex

and a set of labeled edges, where each edge (v,l,w) connects a pair of distinct vertices v,w.

The edges are either directed and labeled ≤ or <, or undirected and labeled 6=.

A model of a TL-graph is an interpretation of the vertex names as elements of a totally

order set T (with strict ordering <), such that all names attached to the same vertex denote

the same element and the interpretations of names attached to distinct vertices satisfy the

constraints expressed by the edge(s), if any, connecting those vertices.

Definition 2 : A TL-graph is consistent is and only if it has at least one model.

Definition 3 : In a TL-graph we call a path a ≤-path if each label li is ≤ or <. A ≤-

path is a <-path if at least one of these labels is <.

Definition 4 : A ≤-path (<-path) of length n from v0 = vn. A TL-graph is acyclic if it

does not contain any ≤-cycle.

Theorem 1 A TL-graph is consistent iff it does not contain any <-cycle, or any ≤-cycle

that has two vertices connected by an edge with label 6=.

2.2.3 Timegraphs

Definition 5 : A timegraph is an acyclic TL-graph partitioned into a set of time chains,

such that each vertex is on one and only one time chain. A time chain is a ≤-path, plus

possibly transitive edges connecting pairs of vertices on the ≤-path.

Distinct chains of a timegraph can be connected by cross-edges (these, and certain axil-

lary edges, will also be called metaedges). Vertices connected by cross-edges are called

cross-connected vertices (or metavertices).

2.3 VModel - A Single State Qualitative Model 9

Figure 2.2: Example of a TL-graph

The construction of a timegraph from a TL-graph consists of four main steps: consis-

tency checking, ranking of the graph, formation of the chains and making all implicit <

relations explicit.

Table 2.1: Task for Creation and Query of TimegraphsTask Algorithm Used Complexity

Checking Consistency Tarjan’s Algorithm and Lin-

ear <, 6= edges search

O(e)

Ranking the Graph DAG-Longest-Paths Algo-

rithm

O(n+e)

Forming the time chains and

the metagraph

— O(n+e)

Dealing with “not equal” re-

lations

Gereveni’s approach O(e 6 =.(e + n +

k)

Querying — O(n+e)

2.3 VModel - A Single State Qualitative Model

Qualitative Reasoning being a fairly new field of research in computer science, not much

has been done in this field and more so in the direction of its application in education.


Among the few works, the most significant has been the contribution of Qualitative Re-

search Group of Northwestern University, who have developed a software Vmodel [4, 6]

which addresses the problem stated above to some extent. The tool provides with visual

representations to help middle-school students to create qualitative models. It also provides

software coaches, which use simple analysis of the model structure plus qualitative simula-

tion to provide feedback and explanations. It is necessary to analyze the software in order

to bring out its limitations which serve as one of the motivations for this work.

2.3.1 Vmodel Ontology

A qualitative model is represented in terms of some elementary entities — processes, basic

stuff, parameters, connectors, controllers, comparisons and causes. Processes represent the

QP theory notion of physical process. Basic stuffs represent objects, groups and substances

in the world. Parameters represent the QP theory notion of quantity. Connectors, Con-

trollers, Comparisons and Causes act as relationships between processes and basic stuff

acting and modifying their parameters.

2.3.2 VModel Advantages and Limitations

VModel is the first work in the direction of developing software for education. It has stu-

dent friendly visual notations which make modelling interesting for students. It allows to

formulate, analyze, test and revise models. Each of the above approaches are crucial to

understanding science. Simplicity of qualitative simulation allows the software to run on

systems with very low processing power.

On the other hand, VModel has several limitations which limit the number of physi-

cal phenomena that can be accurately captured by the model. The qualitative simulation

method used in VModel is very simple. Every process instance is assumed to be active

throughout the simulation. It deals with a single qualitative state, thus avoiding the com-

plexity of branching behaviours and envisioning. Any phenomena which consists of several

processes with a temporal ordering between them cannot be mapped to a vmodel. The tex-

tual explanations of the physical processes lacks fluency of natural language and is imple-

mented in a plug-in format. There is no module which deals with constructions of models

from natural language descriptions (even in controlled language).

Keeping in mind all the advantages of such a software and the limitations in the present

softwares we try to overcome the limitations by proposing a new qualitative model which

addresses many of these issues.

2.3 VModel - A Single State Qualitative Model 11

2.3.3 Extensions to VModel

Based on the analysis of Vmodel, TL-graphs and timegraphs we propose certain extensions

to overcome the limitations and increase the coverage of the tool.

Temporal Ordering

In order to simplify the process of modelling, Vmodel makes an assumption that every pro-

cess instance must be active. It deals with a single qualitative state avoiding the complexity

of branching behaviours and envisioning. However, this severely restricts the space of pro-

cesses which can be represented using it. Any temporal ordering between processes cannot

be imposed. Thus any complex process which consists of a pipeline (sequence) of simple

processes cannot be represented in the model. In order to remove the above limitation we

take note of the TL-graphs and timegraphs described in section 2.2 and 2.3. Initially, we

consider only 3 relations namely ≤t,=t and <t which correspond to precedes,coincides

and strictly precedes relations between the processes respectively. (Such an assumption

reduces the complexities of the algorithms used for simulation and reasoning. The set can

be expanded to include all the thirteen relations of interval algebra. Work in this direction

is aimed at in the future.).

It must be noted here that the algorithms for TL-graph and timegraphs are not directly

applicable to the graph which represents the temporal ordering of the processes in the

model. This is because of the different semantics which changes the notion of consis-

tency defined earlier for TL-graphs. The graph obtained from the processes represents a

sequence by which processes are executed and may contain cycles which represent infinite

(or finite if constraints area attached) sequence of states through which the system passes.

Thus, new modified algorithms need to be presented to account for the semantics as the

TL-graph is no more a DAG (as it was assumed while construction of timegraphs.

Encapsulation

Encapsulation captures the principle of information hiding in which information about

some system is hidden from other systems which are not affected by such information.

It can considered analogous to a black box implementing a particular function, the details

of which are irrelevant. The only relevant thing being the input to the black box and the

output obtained from it. In the real world, complex physical phenomena exhibit encap-

sulation, as it is composed of many simpler physical phenomena, the details of which are

hidden from the external world. For an accurate representation of such phenomena, it is

necessary that the qualitative model used must account for such phenomena.


Let us consider a small example to bring out the necessity and efficacy of encapsulation.

Composition

Compositionality concerns the ability to combine representations for different aspects of

a phenomenon or system to create a representation of the phenomenon or system as a

whole. It is an issue because one goal of qualitative reasoning is to formalize the modeling

process itself. Composition is difficult to implement as two different models with different

frames of reference need to overlap and have a common time of origin and synchronize

accordingly. Thus composition either requires the specification of additional information

for synchronization. However, certain simple composition in which the two models are

temporally independent can be overlapped. Consider for example a model account for

the process of rising and falling of a bathtub and another model which accounts for the

temperature control with processes heating and cooling. In this case, we can compose the

two models which have common set of entities to come up with a coherent composed model

which models the two temporally independent processes. We propose to augment every

attribute of an entity with a composition operator from the set of max,min,sum,avg,priority

to define the semantics of multiple influences on a single attribute.

2.4 Summary

In this chapter, we presented a brief description of few of the topics relevant to the under-

standing of this work. We discussed the basics of temporal logic and its types. We presented

a brief study of research in the area of qualitative modeling over time. As part of this re-

search we presented an in depth analysis of a similar system for qualitative modelling and

explored the advantages of such a software as well as delved into the enhancements which

can be made to improve the utility of the software.

Chapter 3

Qualitative Temporal Model

3.1 Entity-Relationship-Process Model

The Entity-Relationship (ER) Model is a widely used data model for database design. It

provides a convenient graphical representation to view data, relationships and constraints.

An entity is an object that exists in the real world and is distinguishable from other objects.

We express the distinction by associating with each entity a set of attributes that describes

the object. A relationship is an association among several entities. A relationship set is

collection of relationships of the same type, and an entity set is a collection of entities of

the same type.

While the ER model captures the static information of the world, it does not capture the

semantics of changes associated with the attributes of entity instances. Thus, we introduce

an extension which captures the dynamic information. Processes are defined as objects

which exist over an interval of time and affect the attributes of entities in a deterministic

manner. The details of the improvised entity-relation model are discussed below.

3.1.1 Model Ontology

Entity

A physical object in the real world distinguishable from others by a set of attributes (prop-

erties) is called an entity. An entity can represent a thing like a ball, a group/collection of

things like herd or even some substance like water. Attributes are measurable properties of

the entity

14 Qualitative Temporal Model

Relationships

There are various classes of relationships. They are

Comparisons - Various information about parameters is expressed via comparisons i.e.

Greater than, less than and equals.

Connectors - Rather than confining the set to some predefined relations we give an open

hand to the users to define the connectors apart from a small set of relationships. The query

answering system should be able to answer queries based on relationships between various

objects.

Effects - These include Increases and Decreasesand are used to define the effects of pro-

cesses on attributes. , Influences and CounterInfluence are used to represent functional

dependence between two parameters.

TemporalOrder - These include Precedes,Follows and Coincides relations between pro-

cesses. Though there are in reality 13 relationships (in Interval Algebra) possible we take

only a subset to simplify modelling.

Processes

Every process is defined by a set of initial conditions, a set of invariant conditions and

a set of effects. The initial conditions act as a trigger which initiate the simulation of the

process whenever the conditions are satisfied. The process continues to be simulated till the

invariant conditions set are satisfied and in each simulation cycle the effects are executed

which update the values of attributes of entities in the world. To incorporate the temporal

constraints between processes we also impose the condition that a process whose initial

condition is satisfied is simulated only if it follow the previous process executed in the time

graph. The details of the algorithm for state space exploration using the notion of processes

has been discussed in Chapter 4.

3.2 Formal Model

The temporal qualitative models proposed can conveniently model a complex environment

with large number of states in a simple and finite model. The model is based on qualitative

calculus which allows a flexible representation of only the information that is available and

actually needed. In this section, based on the model discussed previously we define the

model formally.

3.2 Formal Model 15

3.2.1 Entity Specification

E = {E1, E2, ....., En} (3.1)

where,

Ei = Ai1 ×Ai2 ×Ai3....×Aik (3.2)

where Aij is the jth attribute of the ith entity

3.2.2 Process Specification

P = {P1, P2, ......, Pm} (3.3)

where,

Pi = ICi × InvCi ×Ei (3.4)

where ICi is the set of initial conditions, InvCi is the set of invariant conditions and Ei is

the set of effects produced by the process Pi.

The grammar for expressing initial and invariant condition is restricted to arithmetic op-

eration i.e.

AP [=, <, >,≤,≥]AP (3.5)

where

AP = Aij[+,−, ∗,÷]AP (3.6)

Every condition is thus a proposition in predicate logic with the attribute values of the

entities as propositional variables.

3.2.3 Temporal Graph Specification

T = G(P,E)

such that

P1(R)P2 ∈ E

if and only if P1 is temporally related to P2 by R where R is one of

{<t (precedes),=t (coincides), 6=t, (excludes) ≤} (3.7)

16 Qualitative Temporal Model

These relations model the point algebra over time. Two processes are said to coincide

if the activity of one implies that of the other. A process P1 is said to precede P2 if the

process P1 must occur before P2. A process P1 is said to not-follow P2 if the process P1

must occur before or coincide with P2. A process P1 is said to exclude P2 if the activity

of P1 implies the inactivity of P2.

3.2.4 Qualitative State

The qualitative state S of the system is defined by

• the states of the entities of the system defined by the values (qualitative) of the at-

tributes of the entities.

• the set of currently active processes in the system. Processes are activated when their

initial conditions are satisfied and their temporal relationship permit so. Once active

they remain so as long as their invariant conditions are satisfied.

State Transition Table - The state transition table captures the transition between states of

the system and can be viewed as a directed graph with nodes corresponding to states of the

system and edges corresponding to the transition between states.

Some of the states may be marked as final state which mark a state where the system

reaches a termination. Such states may semantically correspond to forbidden states. (for

eg. a hazardous state of the three tank system).

3.3 Grammar for Model Specification

We provide a Context Free Grammar to specify the model. All non-terminals are italicized.

The naming of the symbols and the grammar is self-explanatory. Model → EntityList

ProcessList RelationList

EntityList → Entity EntityList ‖ φ

ProcessList → Process ProcessList ‖ φ

RelationList → Relation RelationList ‖ φ

Entity → EntityName AttributeList

AttributeList → Attribute AttributeList ‖ φ

3.4 Summary 17

Attribute → AttributeName AttributeTypeV alue

AttributeTypeV alue → RealV alued ‖ BooleanV alued

RealV alued → real (min‖max‖int)

BooleanV alued → boolean (true‖false)

Process → ProcessName InitialConditions InvariantConditions Effects

InitialConditions → Condition InitialConditions ‖ φ

InvariantConditions → Condition InvariantConditions ‖ φ

Condition → Precedents (<‖>‖=‖<=‖>=‖) Antecedents

Precedent → Expression

Antecedent → Expression

Expression → Attribute ‖ Attribute Operator Expression

Operator → (+ ‖ − ‖ ÷ ‖ ∗)Effect → (EffectType Attribute value ) ‖ (EffectType Attribute)

EffectType → incr‖decr‖assign

Relation → Process1 temporalOP Process2

Process1 → Process

Process2 → Process

temporalOP → (precedes‖follows‖excludes‖coincides)

3.4 Summary

In this chapter, we presented a novel qualitative temporal model which allows us to capture

the behavior of a physical system. The inclusion of processes as a dynamic entity and

the addition of temporal graph to impose an ordering between the processes allows us to

provide a greater flexibility in representing the physics behind the system. Such a model

also allows us to represent the entire behavior (the number of states the system can be is

exponential in the resolution of the attribute values) of the system in a concise and intuitive

nature and serves the requirement of using it as a tool to model the intuition behind a

phenomenon. We also provide a grammar for specifying the model. In the next chapter we

discuss various techniques for reasoning with the information contained in the model.

Chapter 4

Reasoning Algorithms

The primary motivation of proposing a novel qualitative temporal model was to have a con-

cise and intuitive representation of a physical system. In order to extract meaningful and

useful information from the model, we need to compute the qualitative states the system

can be in as well as the various transitions which occur in the system. The state transi-

tion table captures such information. Below we propose certain algorithms which given a

model compute the state transition table, and subsequently use the transition table to extract

generic information about the system and its behaviour.

4.1 State Space Exploration

The problem addressed in this section is the indeterminacy generated by multiple execution

paths in the temporal graph and computing reachability in the state space corresponding to

the model.The algorithm mentioned below generates a state transition table which captures

all possible transitions in the state space of the model and aids in answering reachability

queries. The transition diagram also helps in prediction and tracing the sequence of events

leading to a particular state.

20 Reasoning Algorithms

Algorithm 1 ComputeTransitions (CS)VARIABLES

Global T - State Transition Table

Local CS - Current state init Initial State (IS)

Global TG - Temporal Graph of the processes

Global FS - List of Final States

if CS ∈ FS thenAdd < CS, (CS.AP ), φ > to T

end ifLet AP = List of Active Process in CS

for all SAP such that SAP ⊆ AP doList of Possible Next States LNS = Simulate(S, SAP)

for all NS such that NS ∈ LNS doif NS ∈ T then

Add < CS, (SAP ), NS > to T

elseAdd < CS, (SAP ), NS > to T

ComputeTransitions(NS)

end ifend for

end for

The algorithm 2 described below, given a particular configuration of the system i.e.

the attributed values of all entities and a list of processes to be simulated, simulates the

processes and checks for any inconsistent state that may be arising out of it. For example

: A model simulating a water tub with processes filling and draining, it is not possible

to reason in an consistent manner the behavior of the level of water (with no quantitative

knowledge about the rates of inflow and outflow). However if only one of the processes is

active then the reasoning can be done easily on the level.

The situation can be handled in 2 ways. One is to stop the exploration along any

path which leads to an inconsistent state or explore all the possible consistent states which

can arise. For example in the above case if both the processes are active then the level

of water may be either increasing or decreasing with equal probability and thus both the

possible next states may be considered. The second approach though explores all possible

states of the model, does not give comprehensive guarantee of reachability but rather a

probabilistic estimation of the reachability at best. The algorithm below is for the first

4.2 Cycle Detection in Qualitative State Transition Diagram 21

approach, however by changing the next state computation by not restricting it to a single

possible state and changing the notion of consistency it can easily be transformed to cater

to the second approach.

Algorithm 2 Simulate(S, SAP)state NS

for all Entity Ei dofor all Attribute Aj of Ei do

Let⊕

j denote the combination operator associated with attribute of type Aj

if⊕

k P is consistent where P ∈ SAP ( Semantic definition depending on the

attribute ) thenNS.Ei.Aj =

⊕k P

elsereturn φ

end ifend for

end forreturn NS

4.2 Cycle Detection in Qualitative State Transition Diagram

Cycles in the Qualitative State Transition Diagram represent repetitions or oscillations in

the system. The presence of a cycle in the qualitative state diagram indicates at least one

sequence by which the system remains active over an infinite amount of time. Thus, the

detection of cycles in the system provides useful information about the behaviour of the

system and aids in understanding. The qualitative state transition diagram can be abstracted

to be viewed as a directed graph G(V,E) (Note that such a graph is not a simple graph and

there can be multiple edges between states representing multiple processes which can take

the system from one state to the next). However, since we begin with an initial state, a

simple DFS run with the initial state as the root suffices to detect and report all cycles in

the system.

4.3 Reachability Test

It is interesting to address the problem of reachability between two qualitative states. For an

interactive model, the user must be allowed to ask questions about the which of the states

are actually reachable in the system. Also, another direction to it is to test the reachability

22 Reasoning Algorithms

and report the sequence of events that can take the system from a given state to another

state.

Given a partial (incomplete) configuration of the system, the task is to find out the

states which agree with the configuration and identify the paths by which such states can

be reached from the initial state. Thus, the problem has 2 directions - one is to identify the

states which agree and then identify the paths by which these states can be reached. The first

part can be dealt with by defining the semantics of equality or equivalence of two qualitative

states. With the semantics specified, the task reduces to computing all the qualitative states

the system can be in and test equivalence. The problem of computing all states has been

addresses in the section on State Space Exploration. The second problem of detecting the

path along which the states can be reached translates to a path search in the state transition

diagram generated as a result of State Space Exploration earlier. The path search can again

be interpreted as a DFS. It is to be noted that since, there can be multiple paths to reach a

state including some by looping through a cycle of states, a modified version of the DFS

algorithm needs to be used.

4.3.1 Transitive Closure Computation

Another way of addressing the problem will be to compute the transitive closure of the

state transition diagram and annotate each of the new additional edges added with the path

that takes the state from one to the other. Given this data structure and the pre-processing

required to compute it the problem of reachability of states can actually be addressed in a

linear time. The linearity is due to the state equivalence search over all possible states of

the system.

4.4 Summary

In this chapter, we presented algorithms which extract information from the qualitative

temporal model proposed earlier. Such information is useful in understanding the system.

The information computed using these algorithms is used to generate a user friendly ex-

planation of the system in natural language. All of the algorithms discussed here have

been implemented and incorporated into the software QualSym. In the next chapter, we

discuss various implementation issues associated along with the procedure for generating

explanation of the information computed here in simple English language.

Chapter 5

QualSym : Implementation andSoftware Development

We discuss the various implementation and software development issues associated with

the development of QUALSYM, the software for modelling and reasoning over qualitative

temporal model described in the earlier chapters. It must be understood that the software is

only a prototype and can have a number of extensions to enhance its feature and modelling

capacity. The complete software implementation has been done in Java.

5.1 Visual Drawing Interface

The software provides for a drag and drop drawing interface to allow the user to model the

system visually. There are three basic components which can be drawn visually. They are

the entities, processes and attributes. Relations between processes are depicted as colored

edges between them, such that the color of the edge is indicative of the type of relation

existing between them. The attribute cannot have an independent existence and must exist

with an entity. We use the canvas API in java to implement the drawing interface.

5.2 QML - Qualitative Modeling Language

We propose a new Modelling Language which is a variant of the Extensible Markup Lan-

guage(XML) to represent the model. We choose XML to represent the model because over

the years it has evolved as a standard language for sharing structured information. More-

over, it being extensible allows the users to define mark-up elements, thereby allowing

for the extension of the model easily to include additional properties in future. The exact

24 QualSym : Implementation and Software Development

Figure 5.1: Drawing Interface of QualSym

specification of qualitative model using the language has been discussed in the following

section. An additional advantage of using XML is the availability of APIs for parsing XML

documents in many platforms including Java.

5.2.1 Parsing

The entire model is specified within <qmodel> </qmodel> tags.

Every model consists of three main sections

1. Entity Specification

2. Process Specification

3. Temporal Graph Specification.

Entity Specification

All entities are specified within <entity> </entity> tags. The entity is specified using its

title and type (thing/group of things/substance). Every entity is described using a list of

attributes specified using <attribute> and</attribute> tags. Every attribute is specified

5.2 QML - Qualitative Modeling Language 25

using its name, datatype, initial value and aggregator. In the present version of the software

we cater to only two data types - real and boolean. The real valued data can take up three

values corresponding to the attribute being minimum, maximum or somewhere in between.

The boolean valued attribute can be either true or false.

Process Specification

Every process delimited using <process> and </process> tags is specified using the initial

conditions (declared within <initial conditions> and </initial conditions>), the invariant

conditions (declared within <invariant conditions> and </invariant conditions>) and the

effects (declared within <effects> and </effects>). The specification of each of the above

is self-explanatory and can be easily understood by studying the examples in the Appendix

A.

Temporal Graph Specification

The temporal graph is initialized as having each of the processes corresponding to a node.

In order to add order to the processes edges must be placed in the graph. These edges

are specified within <relation> and </relation> tags. The exact nature of the relation is

specified by operator value which can assume one of coincides, precedes, not-follow and

excludes. These relations model the point algebra over time. Two processes are said to

coincide if the activity of one implies that of the other. A process P1 is said to precede

P2 if the process P1 must occur before P2. A process P1 is said to not-follow P2 if the

process P1 must occur before or coincide with P2. A process P1 is said to exclude P2 if

the activity of P1 implies the inactivity of P2.

5.2.2 Visual Model to QML

Even though the visual model is very effective in representing the system, it is not possible

to capture the dynamic information using a visual model. Thus, the drawing interface

can be used to generate QMLtemplate files. These template files must be modified to add

triggering and invariant conditions to the processes. Also, the effects of the processes on

entities must be specified manually by editing the QML.

5.2.3 QML to Visual Model

We enhance the basic QML to incorporate the position information of the visual objects in

the model. The position information of each object is mention as xpos and ypos tags in the

26 QualSym : Implementation and Software Development

specification of the object. This, allows us to recreate the visual model of the system given

a specification of the system in QML.

5.3 Natural Language Generation

The model specification in terms of entities, processes and a temporal order between them

can be simulated and mapped to the state space of the phenomenon using the algorithm de-

scribed in the previous chapters. Since, each state is basically a description of the attributes

of the entities, the values of the attributes can be plugged into the templates in order to gen-

erate a meaningful textual representation of the phenomenon. It must be noted that though

the text output may not have a good fluency, it certainly will have a high fidelity as the in-

formation is represented is derived directly from the state description without introduction

of any ambiguity.

We provide for 2 level explanation of the system. First, we provide an overview of the

system by describing the entities and the processes. This basically is a textual represen-

tation of the model. Secondly, we also provide an in depth analysis of the model. which

provides explanations in natural language for each states of the model. Since, as discussed

in chapter 4, cycles carry important information about the system. Therefore, we provide

textual descriptions for all the cycles which are detected in the system.

5.4 Querying

The query in the environment can basically be mapped to a reachability study. Thus the

query is mentioned as a configuration of the system. Query answering thus basically in-

volves a search in the state transition diagram of the model for the query state. This has

been previously discussed in Section 4.3.

5.5 Summary

In this chapter, we provide an overview of the actual software implementation and layout

the various components of the software. To review, the main components of the software

are a module for drawing interface, module for parsing QML, module for algorithms and a

module for natural language generation.

Chapter 6

Conclusions and Recommendationsfor Further Work

6.1 Conclusion

In this work, we have proposed a simple and concise model to capture the qualitative be-

haviour of physical systems. In our knowledge this is the first effort to combine temporal in-

formation into a qualitative model with an intent to use it as an aid for teaching school level

physics. We have provided algorithms for extracting information of various resolutions for

the system by generating qualitative state transition diagrams, detecting cyclic/repetitive

behaviour of the system and also checking reachability of a qualitative state for the system.

In order to exhibit the power and utility of the model, we have developed a software

QualSym. QualSym provides a user friendly environment for the task of modeling and

understanding. In order to help users understand the behavior of the system they are mod-

elling we provide for natural language explanations of the model. The complete process of

modelling and reasoning has been shown on two examples in the Appendix A.

6.2 Extension beyond Point Algebra

As discussed previously in section 2.2 there are various frameworks for reasoning about

temporal constraints. In this work, to maintain simplicity we have used Point Algebra.

However, it can be easily seen that most physical processes span over a period of time and

cannot be abstracted to a single time instant. Allen’s Interval Algebra with 13 relations

between intervals is one of the frameworks which provides an algebra over intervals. One

of possible extensions to the present model would be incorporate a tractable subalgebra of

28 Conclusions and Recommendations for Further Work

Allen’s Interval Algebra to model the temporal relation between various processes. This

will allow for a more intuitive way of representing and reasoning about things.

6.3 Compositionality

Compositionality concerns the ability to combine representations for different aspects of a

phenomenon or system to create a representation of the phenomenon or system as a whole.

Composing smaller models to build larger models provides an organized and hierarchical

representation of events. Even though the current version of the software does not support

composition, it is certainly a requirement to model complex environments. Various related

issues such as that of inheritance, interaction between models etc. needs to be looked into.

6.4 Information Extraction from Textual Explanations

Some work in the direction of conversion of a natural language text to a qualitative model

has been done [16, 14]., but still a lot of scope is left. For processing natural language texts

it is necessary to understand the connections between QP theory and natural language. It is

important for understanding the general cognitive plausibility of qualitative models. A few

topics to focus on are

• Investigate forms in which continuous properties can appear in written natural lan-

guage

• Focus on physical quantities found in descriptions of physical processes such as ex-

pansion, movement or transfer

• Results may be used to write grammatical rules of a parser or in the design of infor-

mation extraction algorithms

Appendix A

Examples

We discuss the complete workflow on two of the models in order to bring out the efficacy

of the model in solving other similar problems.

A.1 Oscillations of a Pendulum

A.1.1 Problem Description

We try to model a simple physical phenomenon of the oscillation of a pendulum and show

that various stages of the model. We start by providing the specification of the model in

the form of XML as shown in the diagrams below. The model can be graphically visu-

alized as having four different processes (rising, falling, mean and extrema) acting on an

entity pendulum which is defined by its attributed namely speed, displacement and direc-

tion (Note that there may be other attributes as well such as mass, effective length etc. but

due to simplicity we only consider some of them). On applying the algorithms which were

described earlier we can obtain the state transition diagram which basically represents the

various states through which the system passes.

A.1.2 Visual Model

Shown in the fig A.1 is the visual representation of the pendulum system in the drawing

interface of QualSym.

A.1.3 QML Specification

<qmodel title="Oscillations of Pendulum">

<entity type="Thing" name="pendulum" xpos="407" ypos="274" scale="1.0">

<attribute name="displacement" type="real" init="min" xpos="548" ypos="184" scale="1.0"

30 Examples

Figure A.1: Pendulum System in QualSym

aggregator="sum"></attribute>

<attribute name="speed" type="real" init="max" xpos="257" ypos="187" scale="1.0"


<attribute name="direction" type="boolean" init="false" xpos="413" ypos="430" scale="1.0"

aggregator="and"></attribute>

</entity>

<process name="mean" xpos="393" ypos="20" scale="1.0" initial="true">

<initial_conditions>







</initial_conditions>

<invariant_conditions>




</invariant_conditions>

<effects>

<e type = "assign" entity = "pendulum" attribute = "direction" value = "true"></e>

</effects>

</process>

<process name="rising" xpos="33" ypos="275" scale="1.0" initial="false">


A.1 Oscillations of a Pendulum 31









" value="min">



<effects>

<e type = "decr" entity = "pendulum" attribute = "speed"></e>

<e type = "incr" entity = "pendulum" attribute = "displacement"></e>

</effects>

</process>

<process name="extrema" xpos="407" ypos="599" scale="1.0" initial="false">













<effects>

<e type = "assign" entity = "pendulum" attribute = "direction" value = "false"></e>

</effects>

</process>

<process name="falling" xpos="793" ypos="301" scale="1.0" initial="false">







" value="min">





<effects>

<e type = "incr" entity = "pendulum" attribute = "speed"></e>

<e type = "decr" entity = "pendulum" attribute = "displacement"></e>

</effects>

</process>

<relation type="temporal" process1="rising" operator = "precedes" process2="extrema"></relation>

<relation type="temporal" process1="extrema" operator = "precedes" process2="falling"></relation>

<relation type="temporal" process1="falling" operator = "precedes" process2="mean"></relation>

<relation type="temporal" process1="mean" operator = "precedes" process2="rising"></relation>

</qmodel>

32 Examples

A.1.4 State Description

STATE INFORMATION FOR S0

ENTITIES

ENTITY NAME ATTRIBUTE NAME ATTRIBUTE TYPE ATTRIBUTE VALUE

pendulum displacement real min

pendulum speed real max

pendulum direction boolean false

ACTIVE PROCESSES

Process number 1 : mean


ENTITIES




pendulum direction boolean true

ACTIVE PROCESSES

Process number 1 : rising


ENTITIES


pendulum displacement real max

pendulum speed real min


ACTIVE PROCESSES

Process number 1 : extrema


ENTITIES





ACTIVE PROCESSES

Process number 1 : falling



ENTITIES


pendulum displacement real int



ACTIVE PROCESSES



ENTITIES



pendulum speed real int


ACTIVE PROCESSES


ENTITIES





ACTIVE PROCESSES



ENTITIES





ACTIVE PROCESSES


34 Examples

ENTITIES





ACTIVE PROCESSES


ENTITIES





ACTIVE PROCESSES

Process number 1 : rising

A.1.5 Qualitative State Transition Diagram

CURRENT STATE ———> PROCESSES ———–> NEXT STATES

S0———>mean, ———>S1

S1———>rising, ———>S2 S7 S8 S9

S2———>extrema, ———>S3

S3———>falling, ———>S0 S4 S5 S6

S4———>falling, ———>S0

S6———>falling, ———>S0

S9———>rising, ———>S2

A.1.6 Explanation in Natural Language

OVERVIEW**************

The following is an explanation of the physical phenomena called ”Oscillations of Pendulum”.The model captures the effect of processes mean, rising, extrema and falling on the objects pendu-lum with real valued attribute displacement, real valued attribute speed and binary attribute direc-


tion.

The system can be in 9 number of states. 3 out of the 9 states are terminal states (i.e. they haveno outgoing transition). They are S5, S7, S8,

We provide brief explanation of the processes involved in the system. The process mean isactivated when the displacement of pendulum is equal to minimum , the direction of pendulum isequal to false and the speed of pendulum is equal to maximum. The process once active continuesto remain so as long as the speed of pendulum is equal to maximum , the displacement of pendulumis equal to minimum and the direction of pendulum is equal to false. When the process is active, itchanges the value of direction of pendulum to true .

The process rising is activated when the displacement of pendulum is equal to minimum , thedirection of pendulum is equal to true and the speed of pendulum is equal to maximum. The processonce active continues to remain so as long as the displacement of pendulum is equal to a value inbetween maximum and minimum , the speed of pendulum is greater than minimum and the directionof pendulum is equal to true. When the process is active, it decreases the value of speed of pendulumand increases the value of displacement of pendulum .

The process extrema is activated when the displacement of pendulum is equal to maximum ,the speed of pendulum is equal to minimum and the direction of pendulum is equal to true. Theprocess once active continues to remain so as long as the speed of pendulum is equal to minimum ,the displacement of pendulum is equal to maximum and the direction of pendulum is equal to true.When the process is active, it changes the value of direction of pendulum to false .

The process falling is activated when the speed of pendulum is equal to minimum , the directionof pendulum is equal to false and the displacement of pendulum is equal to maximum. The processonce active continues to remain so as long as the speed of pendulum is greater than minimum , thedisplacement of pendulum is equal to a value in between maximum and minimum and the directionof pendulum is equal to false. When the process is active, it increases the value of speed of pendu-lum and decreases the value of displacement of pendulum .

IN-DEPTH ANALYSIS**************************

The system is initially in the following state.

STATE S0 : For entity pendulum displacement is minimum, speed is maximum and direction isfalse. The state has mean as currently active processes. From this state, the states S1, can be reachedusing processes mean.

We now provide an explanation of all possible transitions that can occur in the system given theinitial state above.

STATE S0 : For entity pendulum displacement is minimum, speed is maximum and direction isfalse. The state has mean as currently active processes. From this state, the states S1, can be reachedusing processes mean.

STATE S1 : For entity pendulum displacement is minimum, speed is maximum and directionis true. The state has rising as currently active processes. From this state, the states S2, S7, S8, S9,

36 Examples

can be reached using processes rising.

STATE S2 : For entity pendulum displacement is maximum, speed is minimum and directionis true. The state has extrema as currently active processes. From this state, the states S3, can bereached using processes extrema.

STATE S3 : For entity pendulum displacement is maximum, speed is minimum and direction isfalse. The state has falling as currently active processes. From this state, the states S0, S4, S5, S6,can be reached using processes falling.

STATE S4 : For entity pendulum displacement is intermediate, speed is maximum and directionis false. The state has falling as currently active processes. From this state, the states S0, can bereached using processes falling.

STATE S5 : For entity pendulum displacement is minimum, speed is intermediate and directionis false. This is a terminal state and has no outgoing transitions.

STATE S6 : For entity pendulum displacement is intermediate, speed is intermediate and direc-tion is false. The state has falling as currently active processes. From this state, the states S0, canbe reached using processes falling.

STATE S7 : For entity pendulum displacement is intermediate, speed is minimum and directionis true. This is a terminal state and has no outgoing transitions.

STATE S8 : For entity pendulum displacement is maximum, speed is intermediate and directionis true. This is a terminal state and has no outgoing transitions.

STATE S9 : For entity pendulum displacement is intermediate, speed is intermediate and direc-tion is true. The state has rising as currently active processes. From this state, the states S2, can bereached using processes rising.

OSCILLATIONS OR REPITIONS IN THE SYSTEM************************************************

Various cycles in the state transition diagram represent oscillations or repition of sequences andare thus important for the understanding of the overall phenomena.. Therefore we provide a conciseexplanation for such cycles in the state transition diagram.

The following is a description of the 1th cycle in the transition table. The cycle constitutesthestates S0->S1->S2->S3->S0. The processes falling take the system from state S3 to state S0.Theprocesses extrema take the system from state S2 to state S3.The processes rising take the systemfrom state S1 to state S2.The processes mean take the system from state S0 to state S1.

The following is a description of the 2th cycle in the transition table. The cycle constitutesthestates S0->S1->S2->S3->S4->S0. The processes falling take the system from state S4 to stateS0.The processes falling take the system from state S3 to state S4.The processes extrema take thesystem from state S2 to state S3.The processes rising take the system from state S1 to state S2.Theprocesses mean take the system from state S0 to state S1.

The following is a description of the 3th cycle in the transition table. The cycle constitutesthestates S0->S1->S2->S3->S6->S0. The processes falling take the system from state S6 to stateS0.The processes falling take the system from state S3 to state S6.The processes extrema take the

A.2 Three Tank Problem 37

system from state S2 to state S3.The processes rising take the system from state S1 to state S2.Theprocesses mean take the system from state S0 to state S1.

A.1.7 Testing Predictions

In order to find out if a particular state of assignment of values to attributes in reachable

from the initial state we specify the query in the form of an assignment to the values to the

variables. For example for the query:

pendulum speed max and

pendulum displacement max

the software will reason to conclude that it is not a reachable state. Had it been a reachable

state the software would have displayed the states which agree with the prediction. The

information about how this state can be reached from any other given state can also be easily

derived by finding all paths between the states in the qualitative state transition diagram.

A.2 Three Tank Problem

A.2.1 Problem Description

The figure below shows a simple system of three couple tanks. This system consists of 6

components: 3 tanks, 2 pipes between them and a pump. The pump fills the first tank with

a liquid. The pipes between the tanks have limited flow rate. The last tank has a hole where

the liquid can run out.

Figure A.2: Three Tank System

38 Examples

A.2.2 Visual Model

The visual model shown in figure A.2 captures the qualitative behaviour of the system.

The model is defined by 3 entities which are the three tanks. Processes transfer12,

transfer23, transfer32, transfer21, pump and drain represent the activities of the sys-

tem. The temporal information is shown by the two exclude edges. The exclude edge be-

tween transfer12 and transfer21 signify that the transfer from tank 1 to tank 2 and tank 2

to tank 1 cannot take place simulataneously. Similarly, from transfer23 and transfer32.

Every entity is associated with an attribute level which basically corresponds to the level

of the liquid in the tank. The level can either be maximum indicating a full tank, minimum

indicating an empty tank or intermediate indicating a partially filled tank. Depending on the

relative levels of the tanks and considering the temporal constraints, the various processes

are activated. The conditions are speficied in the qml file shown in section A.2.3.

EXCLUDES

EXCLUDES

TANK1

TANK2

TANK3

LEVEL

LEVEL

LEVEL

PUMP

TRANS−−FER 1 −−−> 2

TRANS−FER2 −−−> 3

TRANS−FER 2−−−−> 1

TRANS−−FER3 −−−> 2

DRAIN

Figure A.3: Qualitative Model for Three Tank System

A.2.3 QML Specification

<qmodel title="THREE TANK SYSTEM">

<entity type="Thing" name="tank1" xpos="444" ypos="116" scale="1.0">

<attribute name="level" type="real" init="min" xpos="560" ypos="85" scale="1.0"


</entity>





</entity>




</entity>

<process name="pump" xpos="220" ypos="19" scale="1.0" initial="true">









<effects>

<e type="incr" entity="tank1" attribute="level"></e>

</effects>

</process>

<process name="drain" xpos="640" ypos="450" scale="1.0" initial="false">


" value="min">



" value="min">


<effects>

<e type="decr" entity="tank3" attribute="level"></e>

</effects>

</process>

<process name="transfer_1_2" xpos="220" ypos="156" scale="1.0" initial="false">


" entity2="tank2"

attribute2="level">






<effects>



</effects>

</process>








40 Examples



<effects>



</effects>

</process>










<effects>



</effects>

</process>










<effects>



</effects>

</process>

<relation type="temporal" process1="transfer_1_2" operator="excludes" process2="transfer_2_1">

</relation>

<relation type="temporal" process1="transfer_2_3" operator="excludes" process2="transfer_3_2">

</relation>

</qmodel>

A.2.4 State Description


ENTITIES


tank1 level real min




ACTIVE PROCESSES

Process number 1 : pump


ENTITIES


tank1 level real max



ACTIVE PROCESSES

Process number 1 : transfer12


ENTITIES





ACTIVE PROCESSES





ENTITIES





ACTIVE PROCESSES

Process number 1 : drain




42 Examples

ENTITIES


tank1 level real int



ACTIVE PROCESSES





ENTITIES





ACTIVE PROCESSES





ENTITIES





ACTIVE PROCESSES






ENTITIES






ACTIVE PROCESSES





ENTITIES





ACTIVE PROCESSES





ENTITIES





ACTIVE PROCESSES






ENTITIES




44 Examples


ACTIVE PROCESSES




ENTITIES





ACTIVE PROCESSES






ENTITIES





ACTIVE PROCESSES






ENTITIES





ACTIVE PROCESSES





ENTITIES





ACTIVE PROCESSES




ENTITIES





ACTIVE PROCESSES






ENTITIES





ACTIVE PROCESSES




46 Examples

ENTITIES





ACTIVE PROCESSES




ENTITIES





ACTIVE PROCESSES



ENTITIES





ACTIVE PROCESSES




ENTITIES





ACTIVE PROCESSES






ENTITIES





ACTIVE PROCESSES





ENTITIES





ACTIVE PROCESSES





ENTITIES





ACTIVE PROCESSES



ENTITIES

48 Examples





ACTIVE PROCESSES





ENTITIES





ACTIVE PROCESSES





ENTITIES





ACTIVE PROCESSES




A.2.5 Qualitative State Transition Table

CURRENT STATE ———> PROCESSES ———–> NEXT STATES

S0———>pump, ———>S1 S17


S1———>transfer12, ———>S2 S4 S8 S10

S2———>transfer23, transfer21, pump, ———>S3 S9 S5 S21 S7 S11 S13 S16

S3———>drain, transfer32, transfer12, ———>S2 S4 S8 S10 S6 S12 S20 S16

S4———>transfer23, transfer21, pump, ———>S3 S5 S7 S13

S5———>drain, transfer32, transfer12, ———>S2 S4 S6 S12

S6———>drain, transfer23, transfer21, pump, ———>S7 S11 S13 S16



S9———>pump, drain, transfer32, transfer12, ———>S4 S10 S12 S16

S10———>pump, transfer23, ———>S3 S7

S10———>transfer23, ———>S9 S11

S11———>pump, drain, transfer32, transfer12, ———>S4 S10

S11———>drain, transfer32, transfer12, ———>S2 S8

S11———>pump, transfer32, transfer12, ———>S4 S10

S11———>transfer32, transfer12, ———>S2 S8

S11———>pump, drain, transfer12, ———>S4 S10

S11———>drain, transfer12, ———>S2 S8


S12———>pump, drain, transfer21, transfer23, ———>S7 S13


S13———>transfer12, ———>S6 S12

S13———>drain, ———>S14

S14———>transfer12, transfer23, ———>S15 S21 S20 S16

S15———>transfer32, pump, transfer21, drain, ———>S14 S10 S13 S16

S16———>pump, drain, ———>S14

S16———>drain, ———>S10

S16———>pump, ———>S13

S15———>pump, transfer21, drain, ———>S1 S17 S7 S11


S17———>transfer12, ———>S2 S8

S17———>pump, ———>S1

S15———>transfer32, transfer21, drain, ———>S14 S10 S13 S16

S15———>transfer21, drain, ———>S1 S17 S7 S11

S15———>transfer32, pump, drain, ———>S18 S4 S19 S12

S18———>transfer23, ———>S3 S5 S7 S13


50 Examples

S19———>transfer23, ———>S3 S5

S19———>drain, ———>S18

S15———>pump, drain, ———>S14 S10 S13 S16

S15———>transfer32, drain, ———>S2 S6

S15———>drain, ———>S8 S20

S20———>pump, transfer21, drain, ———>S1 S17


S20———>pump, drain, ———>S14 S10

S20———>drain, ———>S8


S20———>transfer21, ———>S7 S11

S20———>pump, ———>S13 S16

S15———>transfer32, pump, transfer21, ———>S14 S10 S13 S16



S15———>transfer21, ———>S3 S9

S15———>transfer32, pump, ———>S18 S4 S19 S12

S15———>pump, ———>S5 S21

S21———>transfer32, pump, drain, ———>S18 S19

S21———>pump, drain, ———>S14 S13


S21———>drain, ———>S10 S16

S21———>transfer32, pump, ———>S18 S19

S21———>pump, ———>S5

S21———>transfer32, ———>S4 S12

S15———>transfer32, ———>S2 S6

S14———>transfer23, ———>S3 S7

S14———>transfer12, ———>S2 S4

S12———>drain, transfer21, transfer23, ———>S7 S13

S12———>pump, transfer21, transfer23, ———>S3 S5

S12———>transfer21, transfer23, ———>S3 S5




S12———>transfer23, ———>S9 S21





S12———>transfer21, ———>S7 S13


S12———>drain, ———>S4

S12———>pump, ———>S19

S11———>transfer12, ———>S6 S20




S11———>transfer32, ———>S4 S10


S11———>drain, ———>S17

S11———>pump, ———>S7

S10———>pump, ———>S14


S9———>pump, transfer32, transfer12, ———>S4 S10 S12 S16


S9———>pump, drain, transfer12, ———>S4 S10 S12 S16

S9———>drain, transfer12, ———>S2 S8 S6 S20





S22———>transfer21, ———>S3 S5

S22———>pump, drain, ———>S18 S19

S22———>drain, ———>S4 S12

S22———>pump, ———>S23

S23———>drain, ———>S18 S19

S9———>transfer12, ———>S24 S15

S24———>pump, drain, transfer21, ———>S1 S17 S14 S10 S7 S11 S13 S16

S24———>drain, transfer21, ———>S1 S17 S14 S10 S7 S11 S13 S16

S24———>pump, transfer21, ———>S3 S9 S5 S21

S24———>transfer21, ———>S3 S9 S5 S21

S24———>pump, drain, ———>S18 S4 S19 S12

S24———>drain, ———>S2 S6

52 Examples

S24———>pump, ———>S23 S22




S9———>transfer32, ———>S4 S10 S12 S16

S9———>pump, drain, ———>S1 S7

S9———>drain, ———>S17 S11

S9———>pump, ———>S3



S8———>pump, ———>S14 S10


S8———>transfer21, ———>S1 S17

S8———>transfer23, ———>S25 S26

S25———>pump, drain, transfer32, ———>S18 S4 S14 S10 S19 S12 S13 S16


S25———>pump, transfer32, ———>S18 S4 S14 S10 S19 S12 S13 S16

S25———>transfer32, ———>S2 S8 S6 S20

S25———>pump, drain, ———>S1 S17 S7 S11

S25———>drain, ———>S0 S26




S26———>transfer32, ———>S2 S8

S26———>pump, drain, ———>S1 S17

S26———>drain, ———>S0

S26———>pump, ———>S7 S11

S25———>pump, ———>S3 S9



S7———>transfer12, ———>S6 S12 S20 S16


S7———>transfer32, ———>S18 S14

S7———>drain, ———>S1


S6———>drain, transfer21, pump, ———>S1 S17 S14 S10



S6———>drain, transfer23, pump, ———>S7 S11 S13 S16


S6———>drain, pump, ———>S18 S4

S6———>pump, ———>S19 S12




S6———>transfer21, ———>S7 S11 S13 S16


S6———>transfer23, ———>S25 S15

S6———>drain, ———>S2



S5———>transfer12, ———>S24 S22


S5———>transfer32, ———>S18 S19

S5———>drain, ———>S14 S13



S4———>pump, ———>S18


S4———>transfer21, ———>S1 S14

S4———>transfer23, ———>S9 S21 S11 S16

S3———>transfer32, transfer12, ———>S2 S4 S8 S10 S6 S12 S20 S16

S3———>drain, transfer12, ———>S2 S4 S8 S10 S6 S12 S20 S16

S3———>transfer12, ———>S24 S22 S15 S21


S3———>transfer32, ———>S18 S14 S19 S13

S3———>drain, ———>S1 S7


S2———>transfer23, pump, ———>S3 S9 S5 S21 S7 S11 S13 S16

S2———>pump, ———>S18 S4

S2———>transfer23, transfer21, ———>S3 S9 S5 S21 S7 S11 S13 S16

S2———>transfer21, ———>S1 S17 S14 S10

S2———>transfer23, ———>S25 S15 S26 S20

54 Examples

A.2.6 Explanation in Natural Language

OVERVIEW**************

The following is an explanation of the physical phenomena called ”THREE TANK SYSTEM”.The model captures the effect of processes pump, drain, transfer12, transfer23, transfer21 andtransfer32 on the objects tank1 with real valued attribute level, tank2 with real valued attributelevel, and tank3 with real valued attribute level.

The system can be in 26 number of states.

We provide brief explanation of the processes involved in the system. The process pump isactivated when the level of tank1 is less than maximum. The process once active continues to remainso as long as the level of tank1 is less than maximum. When the process is active, it increases thevalue of level of tank1 .

The process drain is activated when the level of tank3 is greater than minimum. The processonce active continues to remain so as long as the level of tank3 is greater than minimum. When theprocess is active, it decreases the value of level of tank3 .

The process transfer12 is activated when the level of tank1 is greater than the level of tank2 .The process once active continues to remain so as long as the level of tank1 is greater than the levelof tank2 . When the process is active, it increases the value of level of tank2 and decreases the valueof level of tank1 .




IN-DEPTH ANALYSIS**************************

The system is initially in the following state.

STATE S0 : For entity tank1 level is minimum. For entity tank2 level is minimum. For entity


tank3 level is minimum. The state has pump as currently active processes. From this state, the statesS1, S17, can be reached using processes pump.

We now provide an explanation of all possible transitions that can occur in the system given theinitial state above.

STATE S0 : For entity tank1 level is minimum. For entity tank2 level is minimum. For entitytank3 level is minimum. The state has pump as currently active processes. From this state, the statesS1, S17, can be reached using processes pump.

STATE S1 : For entity tank1 level is maximum. For entity tank2 level is minimum. For entitytank3 level is minimum. The state has transfer12 as currently active processes. From this state,the states S2, S4, S8, S10, can be reached using processes transfer12.

STATE S2 : For entity tank1 level is minimum. For entity tank2 level is maximum. For entitytank3 level is minimum. The state has transfer23,transfer21 and pump as currently active pro-cesses. From this state, the states S3, S9, S5, S21, S7, S11, S13, S16, can be reached using processestransfer23,transfer21 and pump. S1, S17, S14, S10, can be reached using processes transfer21

and pump. S3, S9, S5, S21, S7, S11, S13, S16, can be reached using processes transfer23 andpump. S18, S4, can be reached using processes pump. S3, S9, S5, S21, S7, S11, S13, S16, canbe reached using processes transfer23 and transfer21. S1, S17, S14, S10, can be reached usingprocesses transfer21. S25, S15, S26, S20, can be reached using processes transfer23.

STATE S3 : For entity tank1 level is maximum. For entity tank2 level is minimum. For en-tity tank3 level is maximum. The state has drain,transfer32 and transfer12 as currently activeprocesses. From this state, the states S2, S4, S8, S10, S6, S12, S20, S16, can be reached using pro-cesses drain,transfer32 and transfer12. S2, S4, S8, S10, S6, S12, S20, S16, can be reached usingprocesses transfer32 and transfer12. S2, S4, S8, S10, S6, S12, S20, S16, can be reached usingprocesses drain and transfer12. S24, S22, S15, S21, can be reached using processes transfer12.S18, S14, S19, S13, can be reached using processes drain and transfer32. S18, S14, S19, S13, canbe reached using processes transfer32. S1, S7, can be reached using processes drain.

Similar explanations are generated for 27 states in total. However due to space limitationswe have shown only 3

OSCILLATIONS OR REPITIONS IN THE SYSTEM*******************************************Various cycles in the state transition diagram represent oscillations or repition of sequences and arethus important for the understanding of the overall phenomena.. Therefore we provide a conciseexplanation for such cycles in the state transition diagram.

The following is a description of the 1th cycle in the transition table. The cycle constitutesthestates S2->S3->S2. The processes drain, transfer32 and transfer12 take the system from stateS3 to state S2.The processes transfer23, transfer21 and pump take the system from state S2 tostate S3.

The following is a description of the 2th cycle in the transition table. The cycle constitutesthestates S3->S4->S3. The processes transfer23, transfer21 and pump take the system from stateS4 to state S3.The processes drain, transfer32 and transfer12 take the system from state S3 to

56 Examples

state S4.

The following is a description of the 3th cycle in the transition table. The cycle constitutesthestates S2->S3->S4->S5->S2. The processes drain, transfer32 and transfer12 take the systemfrom state S5 to state S2.The processes transfer23, transfer21 and pump take the system fromstate S4 to state S5.The processes drain, transfer32 and transfer12 take the system from stateS3 to state S4.The processes transfer23, transfer21 and pump take the system from state S2 tostate S3.

The following is a description of the 4th cycle in the transition table. The cycle constitutesthestates S4->S5->S4. The processes drain, transfer32 and transfer12 take the system from stateS5 to state S4.The processes transfer23, transfer21 and pump take the system from state S4 tostate S5.

The following is a description of the 5th cycle in the transition table. The cycle constitutesthestates S2->S3->S4->S5->S6->S7->S2. The processes drain, transfer32 and transfer12 takethe system from state S7 to state S2.The processes drain, transfer23, transfer21 and pump takethe system from state S6 to state S7.The processes drain, transfer32 and transfer12 take thesystem from state S5 to state S6.The processes transfer23, transfer21 and pump take the systemfrom state S4 to state S5.The processes drain, transfer32 and transfer12 take the system fromstate S3 to state S4.The processes transfer23, transfer21 and pump take the system from stateS2 to state S3.

The following is a description of the 25th cycle in the transition table. The cycle constitutes-the states S2->S3->S4->S5->S6->S7->S8->S9->S10->S11->S12->S13->S2. The processesdrain and transfer12 take the system from state S13 to state S2.The processes pump, drain,transfer21 and transfer23 take the system from state S12 to state S13.The processes pump andtransfer12 take the system from state S11 to state S12.The processes transfer23 take the systemfrom state S10 to state S11.The processes pump, drain, transfer32 and transfer12 take the sys-tem from state S9 to state S10.The processes transfer23, transfer21 and pump take the systemfrom state S8 to state S9.The processes drain, transfer32 and transfer12 take the system fromstate S7 to state S8.The processes drain, transfer23, transfer21 and pump take the system fromstate S6 to state S7.The processes drain, transfer32 and transfer12 take the system from stateS5 to state S6.The processes transfer23, transfer21 and pump take the system from state S4 tostate S5.The processes drain, transfer32 and transfer12 take the system from state S3 to stateS4.The processes transfer23, transfer21 and pump take the system from state S2 to state S3.

There are 218 such cycles and explanations are generated for each of them in a similar

manner. Due to space constraints they have not been shown here

A.2.7 Testing Predictions

In order to find out if a particular state of assignment of values to attributes in reachable

from the initial state we specify the query in the form of an assignment to the values to the

variables. The result of the query is displayed as a dialog. For example for the query in the


form of the configuration : tank1 : level : max tank2 : level : int tank3 : level min

The result is is displayed as the state S14 agrees with the configuration. Had it been a

configuration which cannot be reached from the initial state by any sequence of actions, an

appropriate message saying so would have been displayed.

Bibliography

[1] P. V. Beek. Reasoning about qualitative temporal information. Artificial Intelligence, 58:728–734, 1992.

[2] T. Bittner. Approximate qualitative temporal reasoning. Annals of Mathematics and Artificial

Intelligence, 35:39–80, 2001.[3] B. Bredeweg and P. Struss. Current topics in qualitative reasoning. AI Magazine, 24(4):13–16,

December 2004.[4] K. Carney, R. Harris, B. Sherin, K. Forbus, and K. Forbus. A qualitative modeling environ-

ment for middle-school students: A progress report. In St. Mary?s University, pages 65–72,2001.

[5] K. D. Forbus. Qualitative reasoning, 1996.[6] K. D. Forbus, K. Carney, B. L. Sherin, and L. C. U. II. Vmodel: A visual qualitative modeling

environment for middle-school students. In AAAI, pages 820–827, 2004.[7] A. Gerevini and L. Schubert. Efficient algorithms for qualitative reasoning about time. Artifi-

cial Intelligence, 74:207–248, 1995.[8] P. J. Hayes. The second naive physics manifesto. pages 46–63, 1990.[9] T. A. Henzinger. The theory of hybrid automata. pages 278–292. IEEE Computer Society

Press, 1996.[10] M. Huth and M. Ryan. Logic in Computer Science: modelling and reasoning about systems

(Portuguese language edition). Cambridge University Press, 2008.[11] B. K. In. Qualitative simulation, 1986.[12] A. Krokhin, P. Jeavons, and P. Jonsson. Reasoning about temporal relations: The tractable

subalgebras of allen’s interval algebra. Journal of the ACM, 50:2003, 2001.[13] B. Kuipers. Qualitative simulation using time-scale abstraction. International Journal Artifi-

cial Intelligence in Engineering, 3:185–191, 1988.[14] A. Nakhimovsky. Temporal reasoning in natural language understanding: The temporal struc-

ture of the narrative. In In Proceedings of the 3rd European Meeting of the Association for

Computational Linguistics, pages 262–269, 1987.[15] O. Sokolsky, , O. Sokolsky, and H. S. Hong. Qualitative modeling of hybrid systems. In In

Proc. of the Montreal Workshop, 2001.[16] P. R. Sven. Qualitative physics as a component in natural language semantics:.[17] A. Travers, S. Venkatesh, and D. Kieronska. A point-based representation for intervals. pages

169–174, Nov 1995.

60 BIBLIOGRAPHY

[18] L. Vila. A survey on temporal reasoning in artificial intelligence, 1994.[19] M. Vilain, H. Kautz, and P. Beek. Constraint propagation algorithms for temporal reason-

ing. In Readings in Qualitative Reasoning about Physical Systems, pages 377–382. MorganKaufmann, 1986.

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