Axiomatic Constraint Systems for Proof Search Modulo Theories

  • Damien Rouhling
  • Mahfuza Farooque
  • Stéphane Graham-Lengrand
  • Assia Mahboubi
  • Jean-Marc Notin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9322)


Goal-directed proof search in first-order logic uses meta- variables to delay the choice of witnesses; substitutions for such variables are produced when closing proof-tree branches, using first-order unification or a theory-specific background reasoner. This paper investigates a generalisation of such mechanisms whereby theory-specific constraints are produced instead of substitutions. In order to design modular proof-search procedures over such mechanisms, we provide a sequent calculus with meta-variables, which manipulates such constraints abstractly. Proving soundness and completeness of the calculus leads to an axiomatisation that identifies the conditions under which abstract constraints can be generated and propagated in the same way unifiers usually are. We then extract from our abstract framework a component interface and a specification for concrete implementations of background reasoners.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Damien Rouhling
    • 1
  • Mahfuza Farooque
    • 2
  • Stéphane Graham-Lengrand
    • 2
    • 4
  • Assia Mahboubi
    • 3
  • Jean-Marc Notin
    • 2
  1. 1.École Normale Supérieure de LyonLyonFrance
  2. 2.CNRS - École PolytechniquePalaiseau CedexFrance
  3. 3.INRIA, Centre de Recherche en Informatique Saclay-Île de FranceParisFrance
  4. 4.SRI InternationalMenlo ParkUSA

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