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Combining Theories: The Ackerman and Guarded Fragments

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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

Combination of decision procedures is at the heart of Satisfiability Modulo Theories (SMT) solvers. It provides ways to compose decision procedures for expressive languages which mix symbols from various decidable theories. Typical combinations include (linear) arithmetic, uninterpreted symbols, arrays operators, etc. In [7] we showed that any first-order theory from the Bernays-Schönfinkel-Ramsey fragment, the two variable fragment, or the monadic fragment can be combined with virtually any other decidable theory. Here, we complete the picture by considering the Ackermann fragment, and several guarded fragments. All theories in these fragments can be combined with other decidable (combinations of) theories, with only minor restrictions. In particular, it is not required for these other theories to be stably-infinite.

This work is partly supported by the ANR project DECERT.

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Author information

Authors and Affiliations

  1. INRIA Nancy-Grand Est, Nancy, France

    Carlos Areces & Pascal Fontaine

  2. FaMAF, Universidad Nacional de Córdoba, Córdoba, Argentina

    Carlos Areces

  3. Université de Nancy, Loria, Nancy, France

    Pascal Fontaine

Authors
  1. Carlos Areces
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  2. Pascal Fontaine
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Editor information

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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Areces, C., Fontaine, P. (2011). Combining Theories: The Ackerman and Guarded Fragments. 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_4

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  • DOI: https://doi.org/10.1007/978-3-642-24364-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24363-9

  • Online ISBN: 978-3-642-24364-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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