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- W2115998135 abstract "We develop a semantic criterion for a specific rule-based calculus Ax axiomatizing a given logic L to have the so-called bounded proof property. This property is a kind of an analytic subformula property limiting the proof search space. Our main tools are frames and algebras. These structures were used in [23], [11] to construct free algebras of modal logics via coalgebraic methods. In this paper, we use algebras and frames to investigating proof-theoretic aspects of modal logics.We define conservative frames and prove that every finite conservative frame for Ax is a p-morphic image of a finite Kripke frame for L iff Ax has the bounded proof property and L has the finite model property. This result, combined with a one-step of the classical correspondence the- ory, turns out to be quite powerful in case studies. For simple logics such as K, T, K4, S4, etc, establishing basic metatheoretical properties becomes a completely automatic task (the related proof obligations can be instantaneously discharged by current first-order provers). For more complicated logics, some ingenuity is still needed, however we were able to successfully apply our uni- form method to Avron’s cut-free system for GL, to Gor e’s cut-free system for S4.3, and to Ohnishi-Matsumoto’s analytic system for S5.This paper is a slightly extended version of the technical report published in April 2013. The only changes are: a new title and new Sections 1.2 and 9.3." @default.
- W2115998135 created "2016-06-24" @default.
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- W2115998135 date "2013-04-22" @default.
- W2115998135 modified "2023-09-23" @default.
- W2115998135 title "The bounded proof property via step algebras and step frames" @default.
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