Hierarchic Superposition With Weak Abstraction

Peter Baumgartner and Uwe Waldmann

In Maria Paola Bonacina, editor, Automated Deduction, CADE-24, 24nd International Conference on Automated Deduction, LNAI 7898, pages 39-57, Lake Placid, NY, USA, June 9-14, 2013. Springer-Verlag.

Submitted version: [PDF file, © Springer-Verlag]

Extended version of the proceedings article: [PDF file]

Abstract: Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide a new completeness result for the fragment where all background-sorted terms are ground.


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Uwe Waldmann <uwe@mpi-inf.mpg.de>, 2013-12-03.
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