Unification in Modal Theorem Proving

Modal formulas can be proved by translating them into a three-typed logic and then using unification and resolution, with axioms describing properties of the reachability relation among possible worlds. In this paper, we improve on the algorithms in [1], showing that strong skolemisation and occurrence checks are not needed for proving theorems of Q, T, Q4, and S4. We also extend the \u27path logic\u27 approach to S5, give the appropriate unification algorithm, and prove its correctness

Subsumption in Modal Logic

Subsumption has long been known as a technique to detect redundant clauses in the search space of automated deduction systems for classical first order logic. In recent years several automated deduction methods for non-classical modal logics have been developed. This thesis explores, how subsumption can be made to work in the context of these modal logic deduction methods. Many modern modal logic deduction methods follow an indirect approach. They translate the modal sentences into some other target language, and then determine whether there exists a proof in that language, rather than doing deduction in the modal language itself. Consequently, subsumption then needs to focus on the target language, in which the actual proof is done. World Path Logic (WPL) is introduced as a possible target language. Deduction in WPL works very much like in ordinary logic, the only significant difference is the need for a special purpose unification, which unifies world paths under an equational theory (E-unification). Relating WPL to a well understood first order logic of restricted quantification, the properties of WPL, that make deduction work, are examined. The obtained theoretical results are the basis for the following treatment of subsumption in WPL. Subsumption is analyzed treating a clause as a scheme standing for the set of its ground instances. Although the notion of ground instances in WPL is different from ordinary logic, it turns out that - just like in ordinary logic - a clause Cl subsumes another clause C2, if there exists a substitution 6 such that C10 £ C2. Once the special purpose unification has been implemented into a theorem prover to allow for deduction in WPL, existing subsumption tests then work without any further changes

The many-valued theorem prover 3TAP. 3rd. edition

This is the 3TAP handbook. 3TAP is a many-valued tableau-based theorem prover developed at the University of Karlsruhe. The handbook serves a triple purpose: first, it documents the history and development of the prover 3TAP; second, it provides a user\u27s manual, and third it is intended as a reference manual for future developers, including porting hints. This version of the handbook describes 3TAP Version 3.0 as of September 30,1994