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A Unifying Principle for Clause Elimination in First-Order Logic

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Book cover Automated Deduction – CADE 26 (CADE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10395))

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Abstract

Preprocessing techniques for formulas in conjunctive normal form play an important role in first-order theorem proving. To speed up the proving process, these techniques simplify a formula without affecting its satisfiability or unsatisfiability. In this paper, we introduce the principle of implication modulo resolution, which allows us to lift several preprocessing techniques—in particular, several clause-elimination techniques—from the SAT-solving world to first-order logic. We analyze confluence properties of these new techniques and show how implication modulo resolution yields short soundness proofs for the existing first-order techniques of predicate elimination and blocked-clause elimination.

This work has been supported by the Austrian Science Fund (FWF) under projects W1255-N23, S11403-N23, and S11409-N23, by the ERC Starting Grant 2014 SYMCAR 639270, and by the National Science Foundation (NSF) under grant number CCF-1618574.

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Authors and Affiliations

  1. Institute of Information Systems, Vienna University of Technology, Vienna, Austria

    Benjamin Kiesl & Martin Suda

Authors
  1. Benjamin Kiesl
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  2. Martin Suda
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Correspondence to Benjamin Kiesl or Martin Suda .

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Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

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Kiesl, B., Suda, M. (2017). A Unifying Principle for Clause Elimination in First-Order Logic. In: de Moura, L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science(), vol 10395. Springer, Cham. https://doi.org/10.1007/978-3-319-63046-5_17

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  • DOI: https://doi.org/10.1007/978-3-319-63046-5_17

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