DT-an automated theorem prover for multiple-valued first-order predicate logics

Abstract

We describe the automated theorem prover "Deep Thought" (DT). The prover can be used for arbitrary multiple-valued first-order logics, provided the connectives can be defined by truth tables and the quantifiers are generalizations of the classical universal resp. existential quantifiers. DT has been tested with many interesting multiple-valued logics as well as classical first-order predicate logic. DT uses a free-variable semantic tableau calculus with generalized signs. For the existential tableau-rules two liberalized versions are implemented. The system utilizes a static index to control the application of axioms as wells as the search for applicable rules. A dynamic lemma generation strategy and various heuristics to control the tableau expansion and branch closure are integrated into DT. Theoretically, contradiction sets of arbitrary size can be discovered to close a branch.