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EXPERT SYSTEMS Chapter 02 Knowledge Representation Techniques Types of Knowledge • a priori knowledge – comes before knowledge perceived through senses – considered to be universally true • a posteriori knowledge – knowledge verifiable through the senses – may not always be reliable • procedural knowledge – knowing how to do something • declarative knowledge – knowing that something is true or false • tacit knowledge – knowledge not easily expressed by language Knowledge Representation Methods Production Rules Semantic Networks Schemata and Frames Propositional Logic Predicate Calculus Advantages of Production Rules • simple and easy to understand • straightforward implementation in computers possible • formal foundations for some variants Problems with Production Rules • simple implementations are very inefficient • some types of knowledge are not easily expressed in such rules • large sets of rules become difficult to understand and maintain Semantic Networks • graphical representation for propositional information • originally developed by M. R. Quillian as a model for human memory • labeled, directed graph • nodes represent objects, concepts, or situations • labels indicate the name • links represent relationships • the label indicates the type of the relationship Frame represents related knowledge about a subject provides default values for most slots frames are organized hierarchically allows the use of inheritance knowledge is usually organized according to cause and effect relationships slots can contain all kinds of items rules, facts, images, video, comments, debugging info, questions, hypotheses, other frames Frame Advantages • fairly intuitive for many applications – similar to human knowledge organization – suitable for causal knowledge – easier to understand than logic or rules • very flexible Propositional logic • In general a logic is defined by – syntax: what expressions are allowed in the language. – Semantics: what they mean, in terms of a mapping to real world – proof theory: how we can draw new conclusions from existing statements in the logic. • Propositional logic is the simplest. Propositional Logic: Syntax • Symbols (e.g., letters, words) are used to represent facts about the world, e.g., – “P” represents the fact “Andrew likes chocolate” – “Q” represents the fact “Andrew has chocolate” • These are called atomic propositions • Logical connectives are used to represent and: , or: , ifthen: , not: . • Statements or sentences in the language are constructed from atomic propositions and logical connectives. – P Q “Andrew likes chocolate and he doesn’t have any.” – P Q “If Andrew likes chocolate then Andrew has chocolate” Propositional Logic: Semantics • Sentences in propositional logic tell you about what is true or false. – P Q means that both P and Q are true. – P Q means that either P or Q is true (or both) – P Q means that if P is true, so is Q. • This is all formally defined using truth tables. XY XvY TT T TF T FT T FF F We now know exactly what is meant in terms of the truth of the elementary propositions when we get a sentence in the language (e.g., P => Q v R). Proof Theory • For propositional logic useful one is modus ponens: • If A is true and A=> B is true, then conclude B is true. A, A B ————————— B LOGICAL EXPRESSIONS Predicate Calculus • includes a wider range of entities • permits the description of relations and the use of variables. • It also requires an understanding of quantification Predicate Logic • Propositional logic isn’t powerful enough as a general knowledge representation language. • In predicate logic the basic unit is a predicate/ argument structure called an atomic sentence: – likes(alison, chocolate) – Tall (fred) • Arguments can be any of: – constant symbol, such as ‘Richard’ – variable symbol, such as X – function expression, e.g., likes • So we can have: – likes(X, Richard) – friends(motherof(joe), motherof(jim)) Proof and Inference • What can we conclude from the following? – X tall(X) strong(X) – tall(john) – X strong(X) loves(mary, X)