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Lecture 6-2 CS250: Intro to AI/Lisp

Declaring Your Knowledge

Lecture 6-2

November 4th, 1999

CS250/350


Keep your eye on the prize

• Why did we study heuristic search?

• How else can we incorporate knowledge


Designing an Interplanetary Explorer

• Goals for the explorer

• Actions we can take

• Situations that might arise


Telling Your Computer about the World

• What you know

• How to go from what you know to what you don’t know

• Will Rogers


Knowledge Base

Knowledge base:Database :: Knowledge:Data

• KB stores what the computer knows about the world

• Knowledge representation language– How we encode knowledge about the

world– Each bit of knowledge is a sentence


OuRover

• Goals– Gather core samples– Gather rocks– Video sequence of interesting places

• Actions– Drill to depth d– Move forward, backward– Rotate r degrees– Transmit audio/video


Getting through to your computer

• KB Interaction– Tell: Add new sentences to the KB– Ask: Query what’s known (or what follows

from what is known)

• Inference procedure goes from what’s unknown to what’s known


How true is it?

• Valid– Necessarily true under all interpretations in

all worlds– Tautology

A A

• Satisfiable– True sometimes

A B


Knowledge-Based Agents

Agents perceive the world around them Perceptions are recorded in the KB Actions are chosen based on the KB Results of actions are recorded


Levels of Agents

• Knowledge level– What an agent knows– Planetary core samples must be taken at

least 100mm below the surface

• Logical level– Knowledge is encoded at this level– MinDepth(CoreSample,100)

• Implementation level– Inside the machine


Building Knowledge Agents

• Lean on the inference mechanism– Tell agent what it needs to know

• Declarative– Declare the state of the world, and let ‘er

rip

• Adding learning– Reacting to percepts


Separate Domain-Specific from the General


A logic for every season

Increasing complexity, expressive power

Propositional Higher-orderFirst-order


Is this your world?

• if KB1 = then (KB1 KB2) =


Propositional Logic

• Syntax– Propositions– Connectives (, , , , )– ()’s

• Semantics– Implication causation– “A false proposition implies any proposition”


Jumping to propositional conclusions

• How do we reason from what we know to what we don’t?– Inference rules– In propositional logic:

• Modus ponens• And-elimination• And introduction• Double-negation elimination• Unit resolution• Resolution


Horn clauses

• Restricted form:P1 P2 P3 ... Pn Q

• Why is this an advantage?


Wumpus World


Specifying the Wumpus World

• Percepts?

• Actions?

• Goals?


Describing the Wumpus World

• Is the world…– Deterministic– Fully accessible– Static– Discrete


One Environment is Easy

• If we know the environment well, can engineer it

• Range of environments?


Exploring the world

Perceive: [None, None, None, None, None]

Perception: Stench, Breeze, Glitter, Bump, Scream


Move Forward to 2,1


Perception after One Move

Stench: None

Breeze: Yes

Glitter: None

Bump: None

Scream: None


What Does the World Look Like?


Knowledge Representation

• Not just computer readable…

…computer reasonable as well

• Syntax - Rules for building expressions

• Semantics - Relationship between facts in the world and sentences

• Examples?


Entailment

• What follows from what

• Entailment is relationship among sentences– KB entails a

• “Follows” is a relationship among facts in the world

• Inference procedures that generate only entailed sentences is sound


Logical Commitment


;;;; Main Functions on KBs: Tell, Retract, Ask-Each, ;;;; Ask, Ask-Pattern[s]

;;; First we define a very simple kind of knowledge base,;;; literal-kb, that just stores a list of literal sentences.

(defstructure literal-kb "A knowledge base that just stores a set of literal sentences." (sentences '()))

Tell-Ask.lisp I


;;; There are three generic functions that operate on;;; knowledge bases, and that must be defined as methods;;; for each type of knowledge base: TELL, RETRACT, and;;; ASK-EACH. Here we show the implementation for literal-kb;;;; elsewhere you'll see implementations for propositional,;;; Horn, and FOL KBs.

(defmethod tell ((kb literal-kb) sentence) "Add the sentence to the knowledge base." (pushnew sentence (literal-kb-sentences kb) :test #'equal))

(defmethod retract ((kb literal-kb) sentence) "Remove the sentence from the knowledge base." (deletef sentence (literal-kb-sentences kb) :test #'equal))

(defmethod ask-each ((kb literal-kb) query fn) "For each proof of query, call fn on the substitution that the proof ends up with." (declare (special +no-bindings+)) (for each s in (literal-kb-sentences kb) do (when (equal s query) (funcall fn +no-bindings+))))

Tell-Ask.lisp II


;;; There are three other ASK functions, defined below,;;; that are defined in terms of ASK-EACH. These are ;;; defined once and for all here (not for each kind ;;; of KB)."

(defun ask (kb query) "Ask if query sentence is true; return t or nil." (ask-each kb (logic query) #'(lambda (s) (declare (ignore s)) (RETURN-FROM ASK t))))

;;; Omitted pattern-matching ASK’s

Tell-Ask.lisp III


Propositional logic: Straw man for the ages

• “Don’t take a core sample if you’re not on a stable surface”

• How hard is it to compute with propositional logic