Theorem proving for prenex Gödel logic with Delta: checking validity and unsatisfiability

Details Theorem proving for prenex Gödel logic with Delta: checking validity and unsatisfiability Theorem proving for prenex Gödel logic with Delta: checking validity and unsatisfiability

2012-02-28

arxiv.org/abs/1202.6352v2

LMCS 8 (1:20) 2012

Computer Science

Logic in Computer Science

23 pages, accepted for LMCS (Logical Methods in Computer Science)

Scientific paper

10.2168/LMCS-8(1:20)2012

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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