Geodesic
Topological models of propositional logic of problems and propositions
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2022), pp. 25-30 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The propositional fragment $\mathrm{HC}$ of the joint logic of problems and propositions introduced by S. A. Melikhov is considered. Topological models of this logic are constructed and the completeness of the logic $\mathrm{HC}$ with respect to this type of models is shown. Topological models of the logic $\mathrm{H}4$ introduced by S. Artemov and T. Protopopescu are also constructed. 
@article{VMUMM_2022_5_a3,
     author = {A. A. Onoprienko},
     title = {Topological models of propositional logic of problems and propositions},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {25--30},
     year = {2022},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2022_5_a3/}
}
TY  - JOUR
AU  - A. A. Onoprienko
TI  - Topological models of propositional logic of problems and propositions
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2022
SP  - 25
EP  - 30
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2022_5_a3/
LA  - ru
ID  - VMUMM_2022_5_a3
ER  - 
%0 Journal Article
%A A. A. Onoprienko
%T Topological models of propositional logic of problems and propositions
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2022
%P 25-30
%N 5
%U http://geodesic.mathdoc.fr/item/VMUMM_2022_5_a3/
%G ru
%F VMUMM_2022_5_a3
A. A. Onoprienko. Topological models of propositional logic of problems and propositions. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2022), pp. 25-30. http://geodesic.mathdoc.fr/item/VMUMM_2022_5_a3/

[1] Melikhov S. A., A Galois connection between classical and intuitionistic logics. I: Syntax. 2013/17, arXiv: 1312.2575

[2] Melikhov S. A., “A Galois connection between classical and intuitionistic logics. I: Semantics. 2015/18”, arXiv: 1504.03379

[3] Kolmogorov A. N., Matematika i mekhanika: Izbrannye trudy, Nauka, M., 1985

[4] Onoprienko A. A., “Semantika tipa Kripke dlya propozitsionalnoi logiki zadach i vyskazyvanii”, Matem. sb., 211:5 (2020), 98–125 | MR

[5] Onoprienko A. A., “Predikatnyi variant sovmestnoi logiki zadach i vyskazyvanii”, Matem. sb., 213:7 (2022), 97–120 | MR

[6] Fairtlough M., Mendler M., “Propositional lax logic”, Inform. and Comput., 137:1 (1997), 1–33 | DOI | MR

[7] Fairtlough M. V.H., Walton M., Quantified lax logic, Tech. rep. CS-97-11, Univ. of Sheffield, 1997

[8] Artemov S., Protopopescu T., Intuitionistic Epistemic Logic. 2014/16, arXiv: 1406.1582v2 | MR

[9] Goldblatt R., “Cover semantics for quantified lax logic”, J. Logic and Comput., 21:6 (2011), 1035–1063 | DOI | MR

[10] Krupskii V. N., “O modelirovanii znaniya v sotsialnykh setyakh”, L694. Desyatye Smirnovskie chteniya, mat-ly Mezhdunar. nauch. konf. (Moskva, 15–17 iyunya 2017 g.)

[11] Raseva E., Sikorskii R., Matematika metamatematiki, Nauka, M., 1972 | MR

[12] Alexandroff P., “Diskrete raume”, Matem. sb., 2:3 (1937), 501–519

[13] Baron M. E., “A note on the historical development of logic diagrams: Leibniz, Euler and Venn”, The mathematical gazette, 53:384 (1969), 113–125 | DOI

[14] Stone M. H., “Topological representations of distributive lattices and Brouwerian logics”, Časopis pro pěstování matematiky a fysiky, 67:1 (1938), 1–25 | DOI | MR

[15] Tsao-Chen T., “Algebraic postulates and a geometric interpretation for the Lewis calculus of strict implication”, Bull. Amer. Math. Soc., 44:10 (1938), 737–744 | DOI | MR

[16] Tarski A., “Der aussagenkalkul und die topologie”, J. Symbol. Logic, 4:1 (1939), 26–27 | MR

[17] McKinsey J. C.C., “A solution of the decision problem for the Lewis systems S2 and S4, with an application to topology”, J. Symbol. Logic, 6:4 (1941), 117–124 | DOI | MR