Prover for Multiple - ValuedFirst - Order Predicate

We describe the automated theorem prover \Deep Thought" (d DT). The prover can be used for arbitrary multiple-valued rst-order logics, provided the connec-tives can be deened by truth tables and the quantiiers are generalizations of the classical universal resp. ex-istential quantiiers. d DT has been tested with many interesting multiple-valued logics as well as classical rst-order predicate logic. d 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 d DT. Theoretically, contradiction sets of arbitrary size can be discovered to close a branch.