Predicate Logic

Abstract

Predicate logic can be understood as an extension of propositional logic. The additional new concepts include quantifiers, function symbols and predicate symbols. These new notions allow us to describe assertions which cannot be expressed with the available tools of propositional logic. For example, up to this point it was not possible to express that certain “objects” stand in certain relations, or that a property holds for all such objects, or that some object with a certain property exists. Here is a well known example from calculus: For all ε > 0 there exists some n₀, such that for all n ≥ n₀, abs(f(n) − a) < ε. The main concepts here are the verbal constructs for all and exists, as well as the use of functions (abs, f, −) and relations (>, ≥, <).