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Modular Termination and Combinability for Superposition Modulo Counter Arithmetic

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Frontiers of Combining Systems (FroCoS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6989))

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Abstract

Modularity is a highly desirable property in the development of satisfiability procedures. In this paper we are interested in using a dedicated superposition calculus to develop satisfiability procedures for (unions of) theories sharing counter arithmetic. In the first place, we are concerned with the termination of this calculus for theories representing data structures and their extensions. To this purpose, we prove a modularity result for termination which allows us to use our superposition calculus as a satisfiability procedure for combinations of data structures. In addition, we present a general combinability result that permits us to use our satisfiability procedures into a non-disjoint combination method à la Nelson-Oppen without loss of completeness. This latter result is useful whenever data structures are combined with theories for which superposition is not applicable, like theories of arithmetic.

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Authors and Affiliations

  1. LORIA-INRIA Nancy Grand Est, France

    Christophe Ringeissen & Valerio Senni

Authors
  1. Christophe Ringeissen
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  2. Valerio Senni
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Editors and Affiliations

  1. University of Iowa, USA

    Cesare Tinelli

  2. Max-Planck-Institut für Informatik, Campus E 1.4, 66123, Saarbrücken, Germany

    Viorica Sofronie-Stokkermans

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Ringeissen, C., Senni, V. (2011). Modular Termination and Combinability for Superposition Modulo Counter Arithmetic. In: Tinelli, C., Sofronie-Stokkermans, V. (eds) Frontiers of Combining Systems. FroCoS 2011. Lecture Notes in Computer Science(), vol 6989. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24364-6_15

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  • DOI: https://doi.org/10.1007/978-3-642-24364-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24363-9

  • Online ISBN: 978-3-642-24364-6

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