Lesson 13 - Module 6 Knowledge Representation and Logic...

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Module 6 Knowledge Representation and Logic – (First Order Logic) Version 1 CSE IIT, Kharagpur
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6.1 Instructional Objective Students should understand the advantages of first order logic as a knowledge representation language Students should be able to convert natural language statement to FOL statements The student should be familiar with the following concepts of first order logic o syntax o interpretation o semantics o semantics of quantifiers o entailment o unification o Skolemization Students should be familiar with different inference rules in FOL Students should understand soundness and completeness properties of inference mechanisms and the notions of decidability Students should learn in details first order resolution techniques The use of search in first order resolution should be discussed, including some search heuristics At the end of this lesson the student should be able to do the following: Represent a natural language description as statements in first order logic Applying inference rules Implement automated theorem provers using resolution mechanism Version 1 CSE IIT, Kharagpur
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Lesson 13 First Order Logic - I Version 1 CSE IIT, Kharagpur
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6.2.1 Syntax Let us first introduce the symbols, or alphabet, being used. Beware that there are all sorts of slightly different ways to define FOL. 6.2.1.1 Alphabet Logical Symbols: These are symbols that have a standard meaning, like: AND, OR, NOT, ALL, EXISTS, IMPLIES, IFF, FALSE, =. Non-Logical Symbols: divided in: o Constants: ± Predicates: 1-ary, 2-ary, . ., n-ary. These are usually just identifiers. ± Functions: 0-ary, 1-ary, 2-ary, . ., n-ary. These are usually just identifiers. 0-ary functions are also called individual constants . Where predicates return true or false, functions can return any value. o Variables: Usually an identifier. One needs to be able to distinguish the identifiers used for predicates, functions, and variables by using some appropriate convention, for example, capitals for function and predicate symbols and lower cases for variables. 6.2.1.2 Terms A Term is either an individual constant (a 0-ary function), or a variable, or an n-ary function applied to n terms: F(t1 t2 . .tn) [We will use both the notation F(t1 t2 . .tn) and the notation (F t1 t2 . . tn)] 6.2.1.3 Atomic Formulae An Atomic Formula is either FALSE or an n-ary predicate applied to n terms: P(t1 t2 . . tn). In the case that "=" is a logical symbol in the language, (t1 = t2), where t1 and t2 are terms, is an atomic formula. 6.2.1.4 Literals A Literal is either an atomic formula (a Positive Literal ), or the negation of an atomic formula (a Negative Literal ). A Ground Literal is a variable-free literal. Version 1 CSE IIT, Kharagpur
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This note was uploaded on 09/20/2010 for the course MCA DEPART 501 taught by Professor Hemant during the Fall '10 term at Institute of Computer Technology College.

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Lesson 13 - Module 6 Knowledge Representation and Logic...

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