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  • STABLE CANONICAL RULES

  • GURAM BEZHANISHVILI, NICK BEZHANISHVILI, ROSALIE IEMHOFF
  • Journal:
    The Journal of Symbolic Logic / Volume 81 / Issue 1 / March 2016
    Published online by Cambridge University Press:
    09 March 2016, pp. 284-315
    Print publication:
    March 2016
    • Article
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  • We introduce stable canonical rules and prove that each normal modal multi-conclusion consequence relation is axiomatizable by stable canonical rules. We apply these results to construct finite refutation patterns for modal formulas, and prove that each normal modal logic is axiomatizable by stable canonical rules. We also define stable multi-conclusion consequence relations and stable logics and prove that these systems have the finite model property. We conclude the paper with a number of examples of stable and nonstable systems, and show how to axiomatize them.