Geodesic
Recognizability in pre-Heyting and well-composed logics
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 427-434

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In this paper the problems of recognizability and strong recognizavility, perceptibility and strong perceptibility in extensions of the minimal Johansson logic $\mathrm{J}$ [1] are studied. These concepts were introduced in [2, 3, 4]. Although the intuitionistic logic Int is recognizable over $\mathrm{J}$ [2], the problem of its strong recognizability over $\mathrm{J}$ is not solved. Here we prove that Int is strong recognizable and strong perceptible over the minimal pre-Heyting logic Od and the minimal well-composed logic $\mathrm{JX}$. In addition, we prove the perceptibility of the formula $F$ over $\mathrm{JX}$. It is unknown whether the logic $\mathrm{J+F}$ is recognizable over $\mathrm{J}$.
Keywords: Recognizability, strong recognizability, minimal logic, pre-Heyting logic, superintuitionistic logic
Mots-clés : Johansson algebra, Heyting algebra, calculus. 
@article{SEMR_2019_16_a5,
     author = {L. L. Maksimova and V. F. Yun},
     title = {Recognizability in {pre-Heyting} and well-composed logics},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {427--434},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a5/}
}
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L. L. Maksimova; V. F. Yun. Recognizability in pre-Heyting and well-composed logics. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 427-434. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a5/