Knowledge Representation

Knowledge Representation Hypothesis

Knowledge representation is an essential problem of symbolic-based artificial intelligence

• Knowledge Representation Hypothesis (Smith):Any mechanically embodied intelligent process will comprise of structural ingredients, that – will represent the propositional account of knowledge

the overall process exhibits– independently of such a formal semantics will

play formal and causal role in performing the behavior that manifests the knowledge

Knowledge Representation

• In symbolic functionalism we represent intelligence via manipulation of our beliefs about the surrounding world and knowledge we know.

• Therefore we have to address two fundamental issues– how to represent knowledge

– how to implement the process of reasoning

• State space is a space of possible courses of inference when combining – actual beliefs about current world– general knowledge – rules of inference

The Knowledge Level

• Three levels of the Knowledge-based System conceptualization:- system engineering level – physical realization of the system- symbol level – symbol system (program ) specification- knowledge level – knowledge (to be represented)

specification

• Knowledge Level Hypothesis

– There is a distinct computer level lying immediately above the program (symbol level), which is characterized by knowledge as the medium and principle of rationality as the law of behavior.

AI research × Software Engineering

Knowledge Level

Symbol LevelSystem Level

Intelligent Behaviour

Requirements Specification

Functional Specification

System Implementation

What is Knowledge?

• data – primitive verifiable facts, of any representation. Data reflects current world,often voluminous frequently changing.

• information – interpreted data• knowledge – relation among sets of data (information), that

is very often used for further information deduction. Knowledge is (unlike data) general. Knowledge contains information about behavior of abstract models of the world.

• Knowledge Classification:

– according to source: empirical, theoretical– according to orientation: domain, heuristic, inference– according to type: declarative, procedural

Knowledge Representation Schemas

• Logic based representation – first order predicate logic, Prolog

• Procedural representation – rules, production system• Network representation – semantic networks, conceptual

graphs• Structural representation – scripts, frames, objects

Mathematical Logic

• Propositional Logic – – syntactical primitives: , , , , symbols, true, false– rule of inference: de Morgan rule, modus ponens, … – semantic interpretation

rains blows-wind sun-will-shine

• First Order Predicate Logic – – enriched by variables, predicates, functions– quantifiers ,

friends(father(david),father(andrew)) Y friends(Y, petr) X likes(X,ice_cream) X Y Z parent(X,Y) parent(X,Z) siblings(Y,Z)

Mathematical Logic cont’

• inference representation – proof system• rules of inference – example: modus ponens

– if p is true and p q is true, then mp infers q to be true

X(man(X) mortal(X))man(socrates)(man(socrates) mortal(socrates))mortal(socrates)

• rules of inference can be – sound if all conclusions the rule infers logically follows– complete if it infers all conclusions that logically follows

modus ponens is sound but not complete

Mathematical Logic cont’

• inference representation – resolution theorem proving– transform the knowledge system into clausal

normal form (conjunction of disjunction of literals)– add negation of what has to be proved– keep resolve new disjuncts unless you produce an

empty set

dog(X) animal(X) dog(X) animal(X)

(dog(X) animal(X)) (animal(Y) die(Y)) (dog(fido)))(die(fido) 4

-----------------------(dog(Y) die(Y)) 1+2

(die(fido)) 1+2+3

1+2+3+4

1 2 3

Logic Based Financial Advisor

• savings(inadequate) investment(savings)• savings(adequate) income(adequate) investment(stocks)• savings(adequate) income(inadequate) investment(combined) X saved(X) Y dependents(Y) greater(X,5000*Y)

savings(adequate) X saved(X) Y dependents(Y) greater(X, 5000*Y)

savings(inadequate) X earnings(X,steady) Y dependents(Y) greater(X,

(15000+(4000*X)) income(adequate) X earnings(X,steady) Y dependents(Y) greater(X,

(15000+(4000*X)) income(inadequate) X earnings(X,unsteady) income(inadequate)

• saved(22000)• earnings(25000,steady)• dependents(3)

prolog code example

Production System

• procedural representation of knowledge• in the form of if – then rules• inference mechanism is firing the rules• subject of Expert System lecture

‘jug problem’ exampleif small=0 then

small=3

if big=0 and small=3 then

big=3 and small= 0

5l 3l

Conceptual Graphs

• network knowledge representation schema• rooted in association theory of meaning• very much used in the problem of natural language

processing

Conceptual Graph is complete bipartite oriented graph, where each node is either a concept or a relation

between two concepts, there is one or two edges

each going to concepts, and each concept may represent another conceptual graph dog browncolour

Conceptual Graphs

A monkey scratches its ear with a pawn

monkey scratchagent object ear

instrument

pawpart of

part of

Conceptual Graphs

• each concept has got its type and an instance general concept – a concept with a wildcard instance

specific concept – a concept with a concrete instance

• there exists a hierarchy of types subtype:

• concept w is specialisation of concept v iftype(v)>type(w) or instance(w)::type(v)

dog:Emma browncolour

dog:*X browncolour

animal

dog cat

Conceptual Graphs

• canonic conceptual graph is sensible representation of knowledge that can be but does not necessary need to be true

• canonic formation rules formalise rules of inference between two graph for while preserving canonicity – copy – identical cloning of a graph– restriction – substituting a concept in a graph with

its specialisation

– join – joining two graphs via shared concept– simplification – deleting identical relations

Restriction of Concepts

person eatagent object piepiepiepiepiepiepie

girl eatagent object piepiepiepiepiepiepie

person:Sue eatagent object piepiepiepiepiepiepie

girl:Sue eatagent object piepiepiepiepiepiepie

person

Joining Concepts

person eatagent object piepiepiepiepiepiepiegirl:Sue

person eatagent manner piepiepiepiepiepiefastgirl:Sue

person eat

agent object piepiepiepiepiepiepie

agentmanner fast

Simplification of Concepts

person eat

agent object piepiepiepiepiepiepie

agentmanner fast

person eatagent

object piepiepiepiepiepiepie

manner fast

Conceptual Graphs

• FOPL transformation to CG– for each node predicate– general concept variable, specific concept atom

type:instance type(instance) – relation n-ary predicat relation(in1, in2, …, inn)

with arguments conncecting neighbouring concepts– CG is existencionally quantified conjunction of these

predicates

X (dog(emma) color(emma,X) brown(X))

dog:Emma browncolour

Frames

• instance of structured representation (schemes)• static data-structure representing stereotyped

situation • predecessor of object-oriented systems

hotel bedsuperclass:beduse:sleepingsize:kingpart:mattress frame

mattresssuperclass:cushionfirmness:firm

hotel roomspecial of:roomlocation:hotelcontains: hotel chair hotel phone hotel bed hotel phone

special of:phoneuse: calling room servicebilling: through room

hotel chairspecial of:chairlegs:fouruse:sitting

• default slots• daemons – procedural

attachment (infoseek)

Scripts

• Schank’s formalisation of stereotyped sequence of events in a particular context

• knowledge base representation in terms of the situations that the system is supposed to understand

• a restaurant script