Stable canonical rules
Guram Bezhanishvili, Nick Bezhanishvili, Rosalie Iemhoff
Abstract:
We introduce stable canonical rules and prove that each normal modal rule system is axiomatizable by stable canonical rules. This solves an open problem of Jerabek [13, p. 1204]. We apply these results to construct finite refutation patterns for each modal formula that is not derivable in the basic modal logic K, and prove that each normal modal logic is axiomatizable by stable canonical rules. This solves an open problem of Chagrov and Zakharyaschev [11, Ch. 9, p. 332, Prob. 9.5], but our solution is by means of multiple-conclusion rules rather than formulas.
Keywords: Modal logic; Modal rule systems; Axiomatization; Filtration; Modal algebra