What is an inference rule?

Abstract

A general semantic framework that allows the notion of inference to be investigated is introduced. Validity inference and truth inference are in some sense the extremal points of the framework used. The relationship between various types of inference is studied, and their complexity is considered in the context of a number of logics of interest: classical propositional logic, a nonstandard propositional logic, various propositional modal logics, and first-order logic.