Entailment Multipliers: An Algebraic Characterization of Validity for Classical and Modal Logics

We propose a novel algebraic characterisation of the classical notion of validity in terms of boolean rings, called entailment multipliers. We demonstrate the existence of such multipliers and show how they can be used to derive stronger entailment statements. An interesting property of multipliers lies in their behaviour as invariants in a proof, a fact that is used to show how several inference systems can be employed to compute entailment multipliers. A similar characterisation of validity for modal logics is presented.