FOL1 - CS245 Winter 2010 Lecture of Feb 22nd Shai Ben-David...

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Shai Ben-David 1 First Order Logic / Predicate Logic The basic idea of first Order Logic: There are two types of entities: objects and relations (also called properties or predicates) among them. Some informal examples of predicate logic: Intended Meaning Formula Socrates is a Man M ( s ), where M is a property and s is an object Every Man is mortal x, ( M ( x ) T ( x )), where T is the property of being mortal Socrates is mortal T ( s ) So we get the formula: ( M ( s ) ∧ ∀ x ( M ( x ) T ( x ))) T ( s ) Discussing Order Relations: Objects: x,y,z,. .. Relation: R ( x,y ) denoting x < y Intended Meaning Formula R is asymmetric x,y,R ( x,y ) → ¬ R ( y,x ) R is transitive x,y,z, ( R ( x,y ) R ( y,z )) R ( x,z ) Between every two points, there exists a third x,y,R ( x,y ) → ∃ z, ( R ( x,z ) R ( z,y )) Discussing Natural Numbers: Objects: x,y,z,. ..a (denotes 0) Relation: R ( x,y ) denoting
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FOL1 - CS245 Winter 2010 Lecture of Feb 22nd Shai Ben-David...

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