Abstract

The goal of a logic is to define a consequence relation between a set of formulas Γ and, in most cases, an individual formula A. This definition generally takes one of two forms. From a proof theoretic standpoint, A is said to be a consequence of Γ whenever there is a deduction of A from the set Γ, viewed as a set of premises; from a model theoretic standpoint, A is said to be a consequence of Γ whenever A holds in every model that satisfies each formula in Γ.