Hierarchic Superposition With Weak Abstraction

Peter Baumgartner 1 Uwe Waldmann 2, 3
2 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
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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Peter Baumgartner, Uwe Waldmann. Hierarchic Superposition With Weak Abstraction. 24th International Conference on Automated Deduction (CADE-24), Jun 2013, Lake Placid, NY, United States. pp.39-57, ⟨10.1007/978-3-642-38574-2_3⟩. ⟨hal-00931919⟩



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