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arXiv · 1202.6352

Theorem proving for prenex G\"odel logic with Delta: checking validity and unsatisfiability

Matthias Baaz·Agata Ciabattoni·Christian G Fermüller
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Abstract

G\"odel logic with the projection operator Delta (G_Delta) is an important many-valued as well as intermediate logic. In contrast to classical logic, the validity and the satisfiability problems of G_Delta are not directly dual to each other. We nevertheless provide a uniform, computational treatment of both problems for prenex formulas by describing appropriate translations into sets of order clauses that can be subjected to chaining resolution. For validity a version of Herbrand's Theorem allows us to show the soundness of standard Skolemization. For satisfiability the translation involves a novel, extended Skolemization method.

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Matthias Baaz, Agata Ciabattoni, Christian G Fermüller. 2012-02-28. Theorem proving for prenex G\"odel logic with Delta: checking validity and unsatisfiability. https://doi.org/10.2168/lmcs-8(1:20)2012

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