Predication Logic Dr Rahim Kha Assistant Professor Department

Predication Logic Dr. Rahim Kha Assistant Professor Department of Computer Science Abdul Wali Khan University Mardan

Universal Quantifiers § Previous Chapter described the way to make statements about specific objects § Does not allow to make universal statements Example • Each student must hand in course work. • Nobody knows the trouble I seen. • Jim doesn’t know anybody who can sign his bail application

Existential Quantifiers • Sometime we are interested in at least one thing has a particular property • Not necessarily which one Examples • I heard it from one of your friends. • A mad dog has bitten Andy. • Some people prefer logic. Leads to the language called predicate calculus

Predicate calculus • A predicate is a statement with a place for an object • There may be many such places within a single predicate • When filled • Predicates become statements about objects that filled them • We could say that a predicate is a proposition with a gap for an object of some kind.

Example • The Statement __ > 5 is a predicate • Is it a proposition? ? ? x > 5 is a predicate • Adding Quantifiers • there is an x, which is a natural number, such that x > 5’. • E. g Number 6

Existential Quantifier Contd… • Existential quantification may be thought of as a generalized form of disjunction