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Workshop on Proof Theory, Modal Logic and Reflection Principles
October 19, 2017 15:15, Moscow, Steklov Mathematical Institute
 

Student session


On axiomatization and polytime decidability of strictly positive fragments of some modal logics

M. Svyatlovsky
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MP4 192.3 Mb

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M. Svyatlovsky


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Abstract: We call a formula strictly positive, if it is built of propositional variables, conjunction and modal diamond operators. The strictly positive fragment (SP-fragment) of a logic L is the set of all provable in L implications A$\to$B, where A and B are strictly positive formulas. E. V. Dashkov proved that Gödel–Löb provability logic GL and the logic K4 have the same SP-fragments.
We study the SP-fragment of the logic K4.3 of all transitive linear frames. We give two different semantical characterizations of the fragmet. We will present a finite axiomatization of the SP-fragment of K4.3 and prove that it is polytime decidable.

Language: English

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