The predicate version of the joint logic of problems and propositions
Sbornik. Mathematics, Tome 213 (2022) no. 7, pp. 981-1003
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We consider the joint logic of problems and propositions $\mathrm{QHC}$ introduced by Melikhov. We construct Kripke models with audit worlds for this logic and prove the soundness and completeness of $\mathrm{QHC}$ with respect to this type of model. The conservativity of the logic $\mathrm{QHC}$ over the intuitionistic modal logic $\mathrm{QH4}$, which coincides with the ‘lax logic’ $\mathrm{QLL}^+$, is established. We construct Kripke models with audit worlds for the logic $\mathrm{QH4}$ and prove the corresponding soundness and completeness theorems. We also prove that the logics $\mathrm{QHC}$ and $\mathrm{QH4}$ have the disjunction and existence properties.
Bibliography: 33 titles.
Keywords:
nonclassical logics, Kripke semantics.
@article{SM_2022_213_7_a2,
author = {A. A. Onoprienko},
title = {The predicate version of the joint logic of problems and propositions},
journal = {Sbornik. Mathematics},
pages = {981--1003},
publisher = {mathdoc},
volume = {213},
number = {7},
year = {2022},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2022_213_7_a2/}
}
A. A. Onoprienko. The predicate version of the joint logic of problems and propositions. Sbornik. Mathematics, Tome 213 (2022) no. 7, pp. 981-1003. http://geodesic.mathdoc.fr/item/SM_2022_213_7_a2/