Constructive Formalization of Hybrid Logic with Eventualities

  • Christian Doczkal
  • Gert Smolka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7086)


This paper reports on the formalization of classical hybrid logic with eventualities in the constructive type theory of the proof assistant Coq. We represent formulas and models and define satisfiability, validity, and equivalence of formulas. The representation yields the classical equivalences and does not require axioms. Our main results are an algorithmic proof of a small model theorem and the computational decidability of satisfiability, validity, and equivalence of formulas. We present our work in three steps: propositional logic, modal logic, and finally hybrid logic.


hybrid logic eventualities small model theorem decision procedures Coq Ssreflect 


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christian Doczkal
    • 1
  • Gert Smolka
    • 1
  1. 1.Saarland UniversitySaarbrückenGermany

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