Knowledge Representation

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 Intelligent Behaviour Requirements Specification Functional Specification Knowledge Level System Implementation System Level Symbol Level

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 3 2 1

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’ example if 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 colour dog brown

part of agent object monkey scratch ear instrument part of paw Conceptual Graphs A monkey scratches its ear with a pawn

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) colour dog:*X brown colour dog:Emma brown 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 agent object person person eat pie pie pie pie pie pie pie agent object girl eat pie pie pie pie pie pie pie agent object person:Sue eat pie pie pie pie pie pie pie agent object girl:Sue eat pie pie pie pie pie pie pie

Joining Concepts agent object person girl:Sue eat pie pie pie pie pie pie pie agent manner person girl:Sue eat pie pie pie fast pie pie pie agent object pie pie pie pie pie pie pie eat person manner fast agent

Simplification of Concepts agent object pie pie pie pie pie pie pie person eat manner fast agent object pie pie pie pie pie pie pie agent person eat manner fast

Conceptual Graphs • FOPL transformation to CG • for each node  predicate • general concept variable, specific concept  atomtype: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)) colour dog:Emma brown

Frames • instance of structured representation (schemes) • static data-structure representing stereotyped situation • predecessor of object-oriented systems • default slots • daemons – procedural attachment (infoseek) hotelchair special of:chair legs:four use:sitting hotelroom special of:room location:hotel contains: hotel chair hotel phone hotel bed hotelphone special of:phone use: calling room service billing: through room hotelbed superclass:bed use:sleeping size:king part:mattress frame mattress superclass:cushion firmness:firm

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

Knowledge Representation