Toward a More Complete Alloy

  • Timothy Nelson
  • Daniel J. Dougherty
  • Kathi Fisler
  • Shriram Krishnamurthi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7316)

Abstract

Many model-finding tools, such as Alloy, charge users with providing bounds on the sizes of models. It would be preferable to automatically compute sufficient upper-bounds whenever possible. The Bernays-Schönfinkel-Ramsey fragment of first-order logic can relieve users of this burden in some cases: its sentences are satisfiable iff they are satisfied in a finite model, whose size is computable from the input problem.

Researchers have observed, however, that the class of sentences for which such a theorem holds is richer in a many-sorted framework—which Alloy inhabits—than in the one-sorted case. This paper studies this phenomenon in the general setting of order-sorted logic supporting overloading and empty sorts. We establish a syntactic condition generalizing the Bernays-Schönfinkel-Ramsey form that ensures the Finite Model Property. We give a linear-time algorithm for deciding this condition and a polynomial-time algorithm for computing the bound on model sizes. As a consequence, model-finding is a complete decision procedure for sentences in this class. Our work has been incorporated into Margrave, a tool for policy analysis, and applies in real-world situations.

Keywords

Function Symbol Relation Symbol Ground Term Skolem Function Worcester Polytechnic Institute 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Timothy Nelson
    • 1
  • Daniel J. Dougherty
    • 1
  • Kathi Fisler
    • 1
  • Shriram Krishnamurthi
    • 2
  1. 1.Worcester Polytechnic InstituteUSA
  2. 2.Brown UniversityUSA

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