The Tableau - based Theorem Prover 3 TAPVersion 4

Overview 3 T A P is a tableau-based theorem prover for many-valued rst-order logics with sorts (in the two-valued version with equality); it is implemented in Prolog. This paper gives an overview of the system with a special focus on the new features of 3 T A P Version 4.0, including: eecient completion-based equality reasoning , methods for handling redundant axiom sets, utilization of pragmatic information contained in axioms to rearrange the search space, and a graphical user interface for controlling 3 T A P and visualizing its output. 3 T A P has been developed at the University of Karlsruhe. In 1989 the project started in cooperation with the Institute for Knowledge Based Systems of IBM Germany. Since 1992 the system is maintained and improved as part of a new project at the University of Karlsruhe funded by the Deutsche Forschungsge-meinschaft (DFG). 3 T A P is able to handle full rst-order logics with any nite number of truth values. Hierarchical (tree-shaped) sorts attached to terms are supported. In the two-valued case, special handling of the equality predicate is provided. Currently , versions for classical rst-order logic, for a certain three-valued rst-order logic 18] and for a seven-valued propositional logic 11] are speciied. It is possible either to prove a theorem or to try to check the consistency of the axioms. The user speciies the input as a set of axioms and theorems contained in a knowledge base le; the formulae do not have to be in any normal form. \if-then" and \if-then-else" connectives can occur in the input to rearrange the search space such as to reeect their particular pragmatics, that diiers from material implication. Furthermore, an ordering on constant and function symbols can be speciied in the knowledge base. Problems from the TPTP problem library 20] can be directly loaded. They are automatically converted into 3 T A P format.