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Vol. 5(3), 2005 (Section Logic)
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Polynomial Ring Calculus for Logical Inference
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Walter Carnielli
Personal web-page
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Date Posted: March, 28th 2005
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Publication Information
The final version of this paper is published as:
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Walter Carnielli, "Polynomial Ring Calculus for Many-valued Logics". Proceedings of the 35th International Symposium on Multiple-Valued Logic. IEEE Computer Society. Calgary, Canadá. IEEE Computer Society, pp. 20-25, 2005.

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.Abstract
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This paper proposes a  new "all-purpose" algebraic proof method applicable to general truth-functional sentential logics and to some non-truth-functional logics. The method, based on reducing polynomials over finite fields, is particularly apt for finitely-many-valued logics (and for classical propositional logic PC). It can be extended to certain non-finitely valued logics and non-truth-functional logics as well, provided they can  be characterized  by two-valued dyadic semantics. The resulting mechanizable proof method introduced here is of interest for automatic proof theory, and seems also to be appropriate for investigating questions on complexity.
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Last Update: October 28th, 2005
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