Theorem proving for prenex G\"odel logic with Delta: checking validity and unsatisfiability
Abstract
G\"odel logic with the projection operator Delta (GDelta) is an important many-valued as well as intermediate logic. In contrast to classical logic, the validity and the satisfiability problems of GDelta 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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