The relative complexity of NP search problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Proof complexity in algebraic systems and bounded depth Frege systems with modular counting
Computational Complexity
Modal logic
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Good Degree Lower Bounds on Nullstellensatz Refutations of the Induction Principle
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Polynomial Ring Calculus for Many-Valued Logics
ISMVL '05 Proceedings of the 35th International Symposium on Multiple-Valued Logic
Journal of Logic, Language and Information
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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.