Guiding Linear Deductions with Semantics

Guidance is a central issue in Automatic Theorem Proving systems due to the enormity of the search space that these systems navigate. Semantic guidance uses semantic information to direct the path an ATP system takes through the search space. The use of semantic information is potentially more powerful than syntactic information for guidance. This research aimed to discover a method for incorporating semantic guidance into linear deduction systems, in particular model elimination based linear systems. This has been achieved. The GLiDeS pruning strategy is a simple strategy of restricting the model elimination deduction to one where all A-literals are false in the guiding model. This can be easily incorporated into any model elimination based prover. Evaluation of the GLiDeS strategy has shown that when “good guidance” has been achieved, the benefit of this guidance is significant. However attempts to develop a heuristic for predicting which model will provide “good guidance” has been largely unsuccessful. Original Contributions 1. Developed novel strategy (GLiDeS) for applying semantic guidance to full linear deduction systems. 2. Shown that the new GLiDeS strategy is sound but incomplete. 3. Shown that GLiDeS is complete for a small group of problems termed Semantic Horn and that this result is essentially equivalent to renaming [Slagle, 1967]. 4. Implemented system to demonstrate ease of including GLiDeS into an existing linear theorem proving system, PTTP. 5. Evaluated performance of the GLiDeS semantic guidance strategy and concluded that overall the GLiDeS strategy does not provide significant improvement to PTTP’s performance. 6. It has been shown that when good guidance is achieved the improvement in performance is significant. GLiDeS dramatically reduces the amount of search space covered before a proof is found (as reflected by the number of inferences made). In the best case, PTTP covered on average 8 times the search space that GLiDeS covered (See NHN SEQ Table 6.7). Material from this thesis has appeared in the following publications: M. Brown. Selecting Semantics for Use with Semantic Pruning of Linear Deductions, In McKay,Bob and Slaney, J. editor, AI 2002: Advances in Artifical Intelligence. 15th Australian Joint Intelligence Canberra, Australia, December 2002 Proceedings, number 2557 in LNAI. Springer-Verlag, Berlin Heidelberg, Germany, 2002. M. Brown and G. Sutcliffe. PTTP+GLiDeS Semantically Guided PTTP, In D. McAllester, editor, Automated Deduction CADE-17: 17th International Conference on Automated Deduction, Pittsburgh, PA, USA, June 17-20, 2000 Proceedings, p 719, number 1831 in LNAI. Springer-Verlag, New York, USA, 2000. M. Brown and G. Sutcliffe. PTTP+GLiDeS: Guiding Linear Deductions with Semantics. In N. Foo, editor, Advanced Topics in Artifical Intelligence: 12th Australian Joint Conference on Artificial Intelligence, AI’99, number 1747 in LNAI, pages 244–254. Springer-Verlag, 1999.