Abstract
Usual unification-based analytic calculi like connection calculi [3, 10] and free variable semantic tableaux [8, 2] do not achieve a confluent integration of unification in the analytic framework. In consequence, theorem provers based on these calculi require tentative control strategies like iterative-deepening search with backtracking. This results in a tendency to solve repeatedly the same subproblems, which can be prohibitively costly. In this paper, we present an alternative approach achieving a confluent integration of unification in the analytic framework. We present also an extension of this approach to support efficiently equality reasoning. This provides a new unification-based analytic calculus which is refutation complete and confluent for first-order logic with equality and for which simple irrevocable control strategies can be complete. Experimental results obtained so far with an implementation of this calculus are more than encouraging: our prover is able to solve, in a fully automated manner, a large set of test problems with very good performances.
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© 1996 Springer-Verlag Berlin Heidelberg
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Billon, JP. (1996). The disconnection method. In: Miglioli, P., Moscato, U., Mundici, D., Ornaghi, M. (eds) Theorem Proving with Analytic Tableaux and Related Methods. TABLEAUX 1996. Lecture Notes in Computer Science, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61208-4_8
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DOI: https://doi.org/10.1007/3-540-61208-4_8
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