Journal of Automated Reasoning

, Volume 30, Issue 2, pp 121–151 | Cite as

Proof-Search in Intuitionistic Logic with Equality, or Back to Simultaneous Rigid E-Unification

  • Andrei Voronkov
Article
  • 35 Downloads

Abstract

We characterize provability in intuitionistic logic with equality in terms of a constraint calculus. This characterization uncovers close connections between provability in intuitionistic logic with equality and solutions to simultaneous rigid E-unification. We show that the problem of existence of a sequent proof with a given skeleton is polynomial-time equivalent to simultaneous rigid E-unifiability. This gives us a proof procedure for intuitionistic logic with equality modulo simultaneous rigid E-unification. We also show that simultaneous rigid E-unifiability is polynomial-time reducible to intuitionistic logic with equality. Thus, any proof procedure for intuitionistic logic with equality can be considered as a procedure for simultaneous rigid E-unifiability. In turn, any procedure for simultaneous rigid E-unifiability gives a procedure for establishing provability in intuitionistic logic with equality.

intuitionistic logic equality rigid E-unification 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Andrei Voronkov
    • 1
  1. 1.Computing Science DepartmentUppsala UniversityUppsalaSweden

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