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Kherson, May 20-22, 2009 1
Nikolaj S. Nikitchenko
Kyiv National Taras Shevchenko University, Ukraine
Integration of Informatics-Programming
Disciplines on a Base of Composition Nominative Approach
Kherson, May 20-22, 2009 2
Introduction
Students lack a unified view on informatics (computer science)
We will advocate necessity of integrative approach to informatics-programming disciplines (disciplines “around” programming) and present its main methodological aspects and basic notions
Kherson, May 20-22, 2009 3
Specialization-Integration Cycle in Theories Development
Integration
SpecializationSpecialization
Specialization
SpecializationSpecialization
Kherson, May 20-22, 2009 4
Integration of Theories
Traditionally integration means constructing of more general theory or mutual translation of theories
Here integration means to present informatics as a whole having various interconnected aspects and parts
How to achieve this goal?
Kherson, May 20-22, 2009 5
Methodological Principles Principle of universal connection: everything is
connected with something else.
Principle of development from abstract to concrete: development is definitely oriented change of the object (notion) from abstract to concrete (from simple to complex, from a lower level to a higher one).
Principle of triadic development: one of the main schemes of development is specified as a development triad
thesis – antithesis – synthesis.
Principle of unity of theory and practice: theory and practice should be considered as influencing each other.
Kherson, May 20-22, 2009 6
Main Aspects of Subject-Object Relation
Gnoseological (how to cognate the object) Ontological (what parts object consists of) Phenomenological (how the object presents itself
to the subject)
Praxiological (how to work with the object)
Main aspects in the approach: gnoseological and praxiological (theory and practice)
Kherson, May 20-22, 2009 7
Levels of notions and their orientation on the Sphere of Computing
Practice
Theory
Society
Transportation
… … …
Sphere of Education
Computing(Informatization)
Categories
Scientific notions
Formal notions
Levels:
Philosophical,
Scientific,
Mathematical
Kherson, May 20-22, 2009 8
Types of Notions
categories
scientific notions
formal notions
Kherson, May 20-22, 2009 9
Examples of Categories subject and object; abstract and concrete; internal and external; quality, quantity, and measure; essence and phenomenon; individual, general, and particular; whole and part; content and form; cause and effect; etc.
Kherson, May 20-22, 2009 10
Operations over Notions
Projection: Categories Scientific Notions
Formalization:Scientific Notions Formal Notions
Kherson, May 20-22, 2009 11
Slogan of the Approach (methodological level)
Integrity By Development From Abstract to Concrete From Philosophical via
Scientific to Mathematical Level
(vertical integrity) With Integrity on each Level
(horizontal integrity)
Kherson, May 20-22, 2009 12
Expected Results
Net of Notions (Ontology)
on various levels
with relations between them
Philosophical
Scientific
Mathematical
Kherson, May 20-22, 2009 13
Developing Scientific Notions Categories are developed in Philosophy
We develop Scientific Notions
The main notion: information Information:
knowledge presented via external form (that can be stored, copied, proceed, etc.)
Information: projection of categories “form and content”
Data: a form of information
Kherson, May 20-22, 2009 14
Profile of the use of terms “Knowledge”, “Information”, and “Data”
Content Form
Knowledge
Information Data
Kherson, May 20-22, 2009 15
Definition of Informatics (first approximation)
Informatics: science that studies - information processing
- by algorithmic methods- with the use of computers
Three aspects of informatics:- information processing in general- constructivity of such processing- practical realization (with computers)
Kherson, May 20-22, 2009 16
The notion of Language
Developed forms of information, information processing, and their aspects are based on the notion of language
Our slogan (on scientific level):the main notion of informatics is the notion of language (primarily in constructive, formal, communicative, and practical aspects)
Kherson, May 20-22, 2009 17
Developing the Notion of Information Process (descriptive aspect)
Two steps of developments: the triad:
information – information process – name the pentad
information – information process – name –
composition – description
Kherson, May 20-22, 2009 18
Descriptive Pentad for Information Process
naming (nomination)
INFORMATION
PROCESS
NAME
Semantic aspectSyntactical aspect
application
interpretation
grammar
Denotational aspect
DESCRIPTION
COMPOSITION
Kherson, May 20-22, 2009 19
Formalizing the Notion of Language (internal aspects)
Language: Semantic System (Composition System) Syntactical System Denotational System
Our slogan (on mathematical level):the first language models –
Composition Nominative Models
Composition System: Data – Function – Composition
Models of Data Processing Languages
Kherson, May 20-22, 2009 20
Developing the notion of Data
This notion is developed according to the following triads of categories:
whole (W) – parts (P) – synthesis (H as Hierarchy) abstract (A) – concrete (C) – synthesis (S).
Thus, we get 9 levels of data types.
Data structures used in informatics can be specified as concretizations of the considered types of data.
Kherson, May 20-22, 2009 21
Diagram of development of the notion of data
… … …
DATA
Level W (Whole)
Level P (Parts)
Level S(Hierarchy)
P.C – sets
P.S – nominative data (nominats)
H.A
W.A –“black box” W.C –“white box”
P.A – presets
H.C
H.S
Kherson, May 20-22, 2009 22
Nominative Data Types The typology of nominats is based on the
fundamental relation name value
(the first relation of knowledge representation)
Three dichotomies:
- simple values – complex values- simple names – complex names- values are not names – values as names
Kherson, May 20-22, 2009 23
Cube of Nominates Types
Values as Names
Complex Names
Complex Values
Values not Names
Simple Names
Simple Values
Example: A[i,j+1] – complex names, values as names
Kherson, May 20-22, 2009 24
Formalizing the main notions The constructed hierarchical system of notions
is a subject for formalization on a basis of the formulated methodological principles.
In particular, the notions of information and data processes can be formalized as a composition nominative system which consists of semantic, syntactic and denoting systems.
Such systems formalized languages used in programming, computability theory, algebra, and mathematical logic.
Kherson, May 20-22, 2009 25
References
Formal definitions are presented in: Nikitchenko N.S. A Composition Nominative
Approach to Program Semantics.– IT-TR: 1998-020.– Technical University of Denmark.– 1998.– 103 p.
Нікітченко М.С., Шкільняк С.С. Математична логіка та теорія алгоритмів: підручник.– К.: ВПЦ «Київський університет», 2008.– 528 с.
Nikitchenko N.S. Abstract Computability of Non-deterministic Programs over Various Data Structures. LNCS, vol. 2244, Springer 2001.– P. 468–481.
Басараб И.А., Никитченко Н.С., Редько В.Н. Композиционные базы данных. –К.: Либідь, 1992. – 191 с.
Kherson, May 20-22, 2009 26
ConclusionThe proposed approach seems to be useful in
teaching due to the following: it presents an integrated view on informatics and
corresponding disciplines it is based on a small number of principles thus
specifying a clear structure of informatics it proposes various abstraction levels starting from
simple to more elaborate presenting more complex concepts on later stages of education
The main notions are formalized that permits to construct corresponding software systems
Kherson, May 20-22, 2009 27
Thank you!Questions?