Quasi-normal partners of modal logics K4 and GL
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2018), pp. 98-110
Voir la notice de l'article provenant de la source Math-Net.Ru
The paper considers properties of relational models for quasi-normal modal logics containing the transitivity formula $\Box p\to \Box\Box p$ and (or) the Löb formula $\Box(\Box p\to p)\to \Box p$. It is proved that the accessibility relation in refined relational models for quasi-normal companions of such logics as $\bf K4$ and $\bf GL$, as in the normal case, is transitive. Questions concerned axiomatization of the quasi-normal companion of $\bf GL$ under such logics as $\bf K4$ and $\bf K$ are considered. The following fragments are investigated: the fragment of the lattice of quasi-normal logics containing the transitivity formula and (or) the Löb formula and the fragment of the lattice of normal companions of these logics. We consider the function which maps a quasi-normal logic to its normal companion. It is proved that this function is a pseudo-epimorphism.
Mots-clés :
quasi-normal logics
Keywords: general refined frames with distinguished points, lattice of quasi-normal logics.
Keywords: general refined frames with distinguished points, lattice of quasi-normal logics.
@article{VTPMK_2018_4_a7,
author = {I. A. Gorbunov},
title = {Quasi-normal partners of modal logics {K4} and {GL}},
journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
pages = {98--110},
publisher = {mathdoc},
number = {4},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTPMK_2018_4_a7/}
}
I. A. Gorbunov. Quasi-normal partners of modal logics K4 and GL. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2018), pp. 98-110. http://geodesic.mathdoc.fr/item/VTPMK_2018_4_a7/