Knowledge representation methods جلسه سوم

KR is AI bottleneck The most important ingredient in any expert system is knowledge. The power of expert systems resides in the specific, high-quality knowledge they contain about task domains. AI researchers will continue to explore and add to the current repertoire of knowledge representation and reasoning methods. But in knowledge resides the power. Because of the importance of knowledge in expert systems and because the current knowledge acquisition method is slow and tedious, much of the future of expert systems depends on breaking the knowledge acquisition bottleneck and in codifying and representing a large knowledge infrastructure.

Overview of knowledge representation Production rules Semantic networks/web-ontologies Frames Propositional logic Predicate logic Probability (next meeting)

Production rules Production rules are in the form of condition-action pairs: “IF this condition(or premises or antecedent) occurs, THEN some action (or result, or conclusion, or consequence) will (or should) occur.” Ideally, each production rule implements an autonomous chunk of expertise that can be developed and modified independently of other rules Production systems are composed of – production rules – working memory, and – a control Rules can be used as descriptive tools for problem-solving heuristics, replacing a more formal analysis of the problem – incomplete but useful guides to make search decisions Rules can be viewed as simulation of the cognitive behavior of human experts

Advantages and limitations of rules Advantages Rules are easy to understand Inference and explanations are easily derived Modifications and maintenance are relatively easy Uncertainty is easily combined with rules Each rule is usually independent of all others Limitations Complex knowledge requires many, many rules: creating problems in using and maintaining the systems Builders likes rules: preventing the choices of more appropriate representation Systems with many rules may have a search limitation in the control program: difficulty in evaluating rule-based systems and making inferences

semantic network A semantic network is a graphic notation for representing knowledge in patterns ofinterconnected nodes and arcs. It is one way for knowledge visualization and presentation. What is common to all semantic networks is a declarative graphic representation that can be used either to represent knowledge or to support automated systems for reasoning about knowledge.

Semantic networks/web Nodes represent objects and descriptive information about those objects – Objects can be any physical item such as a book, car, desk, a person, and etc. – Nodes can also be concepts, events, or actions, Netwon’s law, election, building house, and etc. – Attributes of an object can also be used as nodes, e.g. color, size, class, age, and etc. Links show the relationship between various objects and descriptive factors – Common links are of “IS-A”, “HAS-A”, “A-KIND-OF”, etc. Inheritance is a useful feature of semantic network – Various characteristics of some nodes can inherit the characteristics of others

Semantic network example

Object, Attributes, and Values Objects, attributes, and values, the O-A-V triplet O-A-V can be used as a common way to represent knowledge The O-A-V triplet can be used to characterize all the knowledge in a semantic net. مثال DBPedia

Advantages and limitations Advantages Flexibility in adding new nodes and links The visualization is easy to understand Inheritance Similarity to that of human information storage Ability to reason and create definition statements between nonlinked nodes XML/RDF standards for definition of nodes and relationships Limitations Inheritance has difficulty with exceptions The perception of the situation can place relevant facts at inappropriate points Procedural knowledge is difficult to represent

Frames A frame is a data structure that includes all the knowledge about a particular object (an application OOP to expert systems) A frame groups values that describe one object The knowledge is partitioned into slots A slot can describe declarative and procedural knowledge

A car frame

Propositional logic a formal way for representing complex statements that can be true or false Propositional logic is the simplest logic propositions is a statement that may be true or false We use letters to show propositions

logical connective The proposition symbols P1, P2 etc are sentences

Wumpus world sentences

Pros and cons of propositional logic Propositional logic is declarative Propositional logic allows partial/disjunctive/negated information –(unlike most data structures and databases) Propositional logic is compositional: –meaning of B 1,1  P 1,2 is derived from meaning of B 1,1 and of P 1,2 Meaning in propositional logic is context- independent (unlike natural language, where meaning depends on context)  Propositional logic has very limited expressive power (unlike natural language) –E.g., cannot say "pits cause breezes in adjacent squares“ except by writing one sentence for each square

Beyond Propositional logic Propositional logic not expressive enough –In Wumpus world we needed to explicitly write every case of Breeze & Pit relation –Facts = propositions –“All squares next to pits are breezy” “Regular” programming languages mix facts (data) and procedures (algorithms) –World[2,2]=Pit –Cannot deduce/compose facts automatically –Declarative vs. Procedural

First-Order Logic Propositional logic has very limited expressive power (unlike natural language) E.g., cannot say “pits cause breezes in adjacent squares” except by writing one sentence for each square Whereas propositional logic assumes world contains facts, first- order logic (like natural language) assumes the world contains –Objects: people, houses, numbers, theories, Ronald McDonald, colors, baseball games, wars, centuries... –Relations: red, round, bogus, prime, multistoried..., brother of, bigger than, inside, part of, has color, occurred after, owns, comes between,... –Functions: father of, best friend, third inning of, one more than, end of –Connectives : , , , ,  –Quantifiers : ,  –Universal:   x : (Man(x) ) Mortal(x) ) –Existential:  y : (Father(y, fred ) )

Syntax of FOL: Basic elements ConstantsKingJohn, 2, NUS,... PredicatesBrother, >,... FunctionsSqrt, LeftLegOf,... Variablesx, y, a, b,... Connectives , , , ,  Equality= Quantifiers , 

Truth in first-order logic Sentences are true with respect to a model and an interpretation Model contains objects (domain elements) and relations among them Interpretation specifies referents for constant symbols → objects predicate symbols → relations function symbols →functional relations An atomic sentence predicate(term 1,...,term n ) is true iff the objects referred to by term 1,...,term n are in the relation referred to by predicate

Syntax of FOL: Basic elements

Wumpus world sentences in FOL