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On the Expressivity and Applicability of Model Representation Formalisms

  • Andreas Teucke
  • Marco Voigt
  • Christoph WeidenbachEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11715)

Abstract

A number of first-order calculi employ an explicit model representation formalism in support of non-redundant inferences and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) clauses, is such a formalism used in the approximation refinement calculus (AR). Our first result is a finite model property for MSLH clause sets. Therefore, MSLH clause sets cannot represent models of clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus (ME), to atoms with disequality constraints, the formalisms used in the non-redundant clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH clause set formalism.

Notes

Acknowledgments

This work was funded by DFG grant 389792660 as part of TRR 248. We thank our reviewers for their valuable comments.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Andreas Teucke
    • 1
    • 2
  • Marco Voigt
    • 1
    • 2
  • Christoph Weidenbach
    • 1
    Email author
  1. 1.Max Planck Institute for InformaticsSaarbrückenGermany
  2. 2.Graduate School of Computer ScienceSaarbrückenGermany

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