Notes 8 Predicate logic and inference ICS 171

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Notes 8: Predicate logic and inference ICS 171 Fall 2006

Notes 8: Predicate logic and inference ICS 171 Fall 2006

Propositional logic is not expressive w Needs to refer to objects in the world,

Propositional logic is not expressive w Needs to refer to objects in the world, w Needs to express general rules n On(x, y) ~ clear(y) n All man are mortal n Everyone who passed age 21 can drink n One student in this class got perfect score n Etc…. w First order logic, also called Predicate calculus allows more expressiveness

Semantics: Models w An interpretation satisfies a wff (sentence) if the wff has the

Semantics: Models w An interpretation satisfies a wff (sentence) if the wff has the value “true” under the interpretation. w An interpretation that satisfies a wff is a model of that wff w Any wff that has the value “true” under all interpretations is valid w Any wff that does not have a model is inconsistent or unsatisfiable w If a wff w has a value true under all the models of a set of sentences delta then delta logically entails w

Example of models w w w The formulas: On(A, F 1) Clear(B) and Clear(C)

Example of models w w w The formulas: On(A, F 1) Clear(B) and Clear(C) On(A, F 1) Clear(B) or Clear(A) Clear(B) Clear(C) Possible interpretations which are models: On = {<B, A>, <A, floor>, <C, Floor>} Clear = {<C>, <B>}

Modeling a domain; Conceptualization w The kinship domain: n n object are people Properties

Modeling a domain; Conceptualization w The kinship domain: n n object are people Properties include gender and they are related by relations such as parenthood, brotherhood, marriage n predicates: Male, Female (unary) Parent, Sibling, Daughter, Son. . . n Function: Mother Father

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