Geodesic
Perceptibility in pre-Heyting logics
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1064-1072

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is dedicated to problems of perceptibility and recognizability in pre-Heyting logics, that is, in extensions of the minimal logic J satisfying the axiom $\neg\neg (\bot\rightarrow p)$. These concepts were introduced in [8, 11, 10]. The logic Od and its extensions were studied in [5, 14] and other papers. The semantic characterization of the logic Od and its completeness were obtained in [5]. The formula F and the logic JF were studied in [12]. It was proved that the logic JF has disjunctive and finite-model properties. The logic JF has Craig's interpolation property (established in [17]). The perceptibility of the formula F in well-composed logics is proved in [14]. It is unknown whether the formula F is perceptible over J [8]. We will prove that the formula F is perceptible over the minimal pre-Heyting logic Od and the logic OdF is recognizable over Od.
Keywords: Recognizability, perceptibility, minimal logic, pre-Heyting logic, superintuitionistic logic
Mots-clés : Johansson algebra, Heyting algebra, calculus. 
@article{SEMR_2020_17_a26,
     author = {L. L. Maksimova and V. F. Yun},
     title = {Perceptibility in {pre-Heyting} logics},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1064--1072},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a26/}
}
TY  - JOUR
AU  - L. L. Maksimova
AU  - V. F. Yun
TI  - Perceptibility in pre-Heyting logics
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2020
SP  - 1064
EP  - 1072
VL  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2020_17_a26/
LA  - en
ID  - SEMR_2020_17_a26
ER  - 
%0 Journal Article
%A L. L. Maksimova
%A V. F. Yun
%T Perceptibility in pre-Heyting logics
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2020
%P 1064-1072
%V 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2020_17_a26/
%G en
%F SEMR_2020_17_a26
L. L. Maksimova; V. F. Yun. Perceptibility in pre-Heyting logics. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1064-1072. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a26/