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International Symposium on Frontiers of Combining Systems

FroCoS 2013: Frontiers of Combining Systems pp 214–228Cite as

Non-cyclic Sorts for First-Order Satisfiability

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8152))

Abstract

In this paper we investigate the finite satisfiability problem for first-order logic. We show that the finite satisfiability problem can be represented as a sequence of satisfiability problems in a fragment of many-sorted logic, which we call the non-cyclic fragment. The non-cyclic fragment can be seen as a generalisation of the effectively propositional fragment (EPR) in the many-sorted setting. We show that the non-cyclic fragment is decidable by instantiation-based methods and present a linear time algorithm for checking whether a given clause set is in this fragment. One of the distinctive features of our finite satisfiability translation is that it avoids unnecessary flattening of terms, which can be crucial for efficiency. We implemented our finite model finding translation in iProver and evaluated it over the TPTP library. Using our translation it was possible solve a large class of problems which could not be solved by other systems.

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Authors and Affiliations

  1. School of Computer Science, The University of Manchester, United Kingdom

    Konstantin Korovin

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  1. Konstantin Korovin
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Editors and Affiliations

  1. LORIA, Inria Nancy Grand Est, Université de Lorraine, 615 rue du Jardin Botanique, 54602, Villers-les-Nancy, France

    Pascal Fontaine

  2. LORIA, Inria Nancy Grand Est, 615 rue du Jardin Botanique, 54602, Villers-lès-Nancy, France

    Christophe Ringeissen

  3. School of Computer Science, The University of Manchester, Oxford Rd, Kilburn Building, M13 9PL, Manchester, UK

    Renate A. Schmidt

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Korovin, K. (2013). Non-cyclic Sorts for First-Order Satisfiability. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds) Frontiers of Combining Systems. FroCoS 2013. Lecture Notes in Computer Science(), vol 8152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40885-4_15

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  • DOI: https://doi.org/10.1007/978-3-642-40885-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40884-7

  • Online ISBN: 978-3-642-40885-4

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