Kripke semantics for the logic of problems and propositions
Sbornik. Mathematics, Tome 211 (2020) no. 5, pp. 709-732
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In this paper we study the propositional fragment $\mathrm{HC}$ of the joint logic of problems and propositions introduced by Melikhov. We provide Kripke semantics for this logic and show that $\mathrm{HC}$ is complete with respect to those models and has the finite model property. We consider examples of the use of $\mathrm{HC}$-models usage. In particular, we prove that $\mathrm{HC}$ is a conservative extension of the logic $\mathrm{H4}$. We also show that the logic $\mathrm{HC}$ is complete with respect to Kripke frames with sets of audit worlds introduced by Artemov and Protopopescu (who called them audit set models).
Bibliography: 31 titles.
Keywords:
non-classical logics, Kripke semantics.
@article{SM_2020_211_5_a3,
author = {A. A. Onoprienko},
title = {Kripke semantics for the logic of problems and propositions},
journal = {Sbornik. Mathematics},
pages = {709--732},
publisher = {mathdoc},
volume = {211},
number = {5},
year = {2020},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2020_211_5_a3/}
}
A. A. Onoprienko. Kripke semantics for the logic of problems and propositions. Sbornik. Mathematics, Tome 211 (2020) no. 5, pp. 709-732. http://geodesic.mathdoc.fr/item/SM_2020_211_5_a3/