Studia Logica

, Volume 69, Issue 1, pp 59-96

First online:

Free-Variable Tableaux for Propositional Modal Logics

  • Bernhard BeckertAffiliated withInst. for Logic, Complexity and Deduction Systems, University of Karlsruhe
  • , Rajeev GorÉAffiliated withAutomated Reasoning Project, Australian National University

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Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux.

automated deduction modal logics modal theorem proving free-variable tableaux