THEOREM PROVING FOR PRENEX GODEL LOGIC WITH Delta: CHECKING VALIDITY AND UNSATISFIABILITY
First-order Godel logic with the projection operator Delta (G(infinity)(Delta)) is an important many-valued as well as intermediate logic. In contrast to classical logic, the validity and the satisfiability problems of G(infinity)(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.
theorem proving godel logic resolution herbrand's theorem skolemization delta modality fuzzy logic chaining calculus