Predicate Logic - Stanford University

CHAPTER14FF FFPredicateLogicWe now turn our attention to a generalization of propositional Logic , called predi-cate, or first-order, Logic . predicates are functions ofzero or more variables thatreturn Boolean values. Thus predicates can be true sometimes and false sometimes,depending on the values of their arguments. For example, we shall find in predicatelogic atomic operands such ascsg(C, S, G). Here,csgis the Predicate name, andC,S, andGare arguments. We can think of this expression as a representationin Logic of the database relation Course-Student-Grade of Fig. It returns thevalueTRUE whenever the values ofC,S, andGare such that studentSgot gradeGin courseC, and it predicates as atomic operands, instead of propositional variables, givesus a more powerful language than expressions involving onlypropositions.

or expressions that we assume are true: r → u (“If it rains, then Joe takes his umbrella”), u → w¯ (“If Joe takes an umbrella, then he doesn’t get wet”), and r¯→ w¯ (“If it doesn’t rain, Joe doesn’t get wet”). What is true for Joe is also true for Mary, and Sue, and Bill, and so on. Thus

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