Deciding Satisfiability of Positive Second Order Joinability Formulae

  • Sébastien Limet
  • Pierre Pillot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4246)


This paper deals with a class of second order formulae where the only predicate is joinability modulo a conditional term rewrite system, first order variables range over ground terms and second order variables are interpreted as relations on ground terms (i.e. sets of tuples of ground terms). We define a generic algorithm that decides the satisfiability of positive second order joinability formulae when an algorithm is known to finitely represent solutions of first order formulae. When the answer is positive, the algorithm computes one particular instance for the second order variables. We apply this technique to the class of positive second order pseudo-regular formulae. The result is then a logic program that represents the instance of the second order variables. We define a transformation to translate this instance into a CTRS. This result can be used to automatically synthesize a program that defines a relation from its specification.


Logic Program Order Variable Predicate Symbol Horn Clause Ground Term 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sébastien Limet
    • 1
  • Pierre Pillot
    • 1
  1. 1.LIFOUniversité d’OrléansFrance

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