**3 Propositional Calculus—Predicate Logic And Fuzzy Logic**

*Timothy J. Ross**University of New Mexico*

**3.1 Predicate Logic**

In classical predicate logic, a simple proposition, P, is a linguistic statement contained within a universe of propositions which can be identified as being strictly true or strictly false. The veracity (truth) of the proposition, P, can be assigned a binary truth value, called T(P), just as an element in a universe is assigned a binary quantity to measure its membership in a particular set. For binary (Boolean) predicate logic, T(P) is assigned a value of 1 (truth) or 0 (false). If U is the universe of all propositions, then T is a mapping of these propositions to the binary quantities (0, 1), or

*T:U* → {0,1}

Now let P and Q ...