Theorem Proving and Model Building with the Calculus KE

A Prolog implementation of a new theorem-prover for rst-order classical logic is described. The prover is based on the calculus KE and the rules used for analysing quantiiers in free variable semantic tableaux. A formal speciication of the rules used in the implementation is described, for which soundness and completeness is straightforwardly veriied. The prover has been tested on the rst 47 problems of the Pelletier set, and its performance compared with a state of the art semantic tableaux theorem-prover. It has also been applied to model building in a prototype system for logical animation, a technique for symbolic execution which can be used for validation. The interest of these experiments is that they demonstrate the value of certain`characteristics' of the KE calculus, such as the signiicant space-saving in theorem-proving, the mutual inconsistency of open branches in KE trees, and the relation of the KE rules tòtraditional' forms of reasoning.

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