PP201408: Bezhanishvili, Guram and Bezhanishvili, Nick and Iemhoff, Rosalie (2014) Stable canonical rules. [Report]

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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 multipleconclusion rules rather than formulas.
Item Type:  Report 

Report Nr:  PP201408 
Series Name:  Prepublication (PP) Series 
Year:  2014 
Uncontrolled Keywords:  Modal logic; Modal rule systems; Axiomatization; Filtration; Modal algebra 
Subjects:  Logic 
Depositing User:  Nick Bezhanishvili 
Date Deposited:  12 Oct 2016 14:37 
Last Modified:  12 Oct 2016 14:37 
URI:  https://eprints.illc.uva.nl/id/eprint/496 
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