A logic that includes the simpler propositional logic plus individual variables (x, y, z, etc. ), individual constants ( a, b, c, etc. -- these are the same as proper names), predicate variables (P, Q, R, S, etc) these range over monadic, or “one-place”, predicates like “is red”, “jumps,” etc. , dyadic, or “two-place”, predicates like “is the sister of,” “is the square root of,” and so on with three, four, etc. Place predicates, and the universal and existential quantifiers. For example, (x) (Px) means “For every x, Px” or “For every x, P is true of X” (note that “(x)” means “for every x. . . . ”--this is the universal quantifier. Similarly, (x) (Px Qx) means “For every x, if Px, then Qx” or “All Ps are Qs. ” The existential quantifier -- Ex -- means “For some x”, as for example Ex (Px) means “For some x, Px” or “There exists an x such that P is true of it. ” Predicate logic is often developed with the additional of a relational constant, identity (=). Predicate logic is a first order logic in that there is quantification over individuals but not over predicates.