Geodesic
Branching-time type operators on finite pseudo-Boolean algebras
Algebra i logika, Tome 47 (2008) no. 4, pp. 509-519.

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Branching-time type operators on pseudo-Boolean algebras (PBAs) are considered. It is proved that on a finite PBA, every operator of this type is defined by a subset of points on a finite frame presenting that PBA.
Mots-clés : pseudo-Boolean algebra
Keywords: branching-time type operator, finite frame. 
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     title = {Branching-time type operators on finite {pseudo-Boolean} algebras},
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     url = {http://geodesic.mathdoc.fr/item/AL_2008_47_4_a6/}
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A. D. Yashin. Branching-time type operators on finite pseudo-Boolean algebras. Algebra i logika, Tome 47 (2008) no. 4, pp. 509-519. http://geodesic.mathdoc.fr/item/AL_2008_47_4_a6/

[1] Kh. Raseva, R. Sikorskii, Matematika metamatematiki, Nauka, M., 1972 | MR

[2] L. L. Esakia, Algebry Geitinga, Metsniereba, Tbilisi, 1985 | MR | Zbl

[3] D. P. Dubhashi, “On decidable varieties of Heyting algebras”, J. Symb. Log., 57:3 (1992), 988–991 | DOI | MR | Zbl

[4] A. Chagrov, M. Zakharyaschev, Modal Logics, Oxford Logic Guides, 35, Clarendon Press, Oxford, 1997 | MR | Zbl

[5] S. K. Klini, Vvedenie v metamatematiku, Inostr. lit-ra, M., 1959

[6] Ya. S. Smetanich, “O polnote ischisleniya vyskazyvanii s dopolnitelnoi operatsiei ot odnoi peremennoi”, Tr. Mosk. matem. ob-va, 9, 1960, 357–371 | Zbl

[7] Ya. S. Smetanich, “Ob ischisleniyakh vyskazyvanii s dopolnitelnoi operatsiei”, Dokl. AN SSSR, 139:2 (1961), 309–312 | MR | Zbl

[8] D. P. Skvortsov, “Ob intuitsionistskom ischislenii vyskazyvanii s dopolnitelnoi logicheskoi svyazkoi”, Issledovaniya po neklassicheskim logikam i formalnym sistemam, Nauka, M., 1983, 154–173 | MR

[9] A. D. Yashin, “Modifitsirovannaya okrestnostnaya semantika dlya logiki Kaminskogo”, Vestnik MGU. Ser. 1. Matem., mekh., 1998, no. 2, 8–11 | MR | Zbl

[10] J. P. Burgess, “Decidability for branching time”, Stud. Log., 39:2–3 (1980), 203–218 | DOI | MR | Zbl

[11] S. McCall, “The strong future tense”, Notre Dame J. Formal Logic, 20:3 (1979), 489–504 | DOI | MR | Zbl

[12] W. B. Ewald, “Intuitionistic tense and modal logic”, J. Symb. Log., 51:3–4 (1986), 166–179 | DOI | MR | Zbl

[13] M. K. Valiev, “Ob aksiomatizatsii logiki diskretnogo razvetvlennogo vremeni”, Materialy 8-i Vsesoyuz. konf. “Logika i metodologiya nauki”, M., 1982, 20–22

[14] A. G. Dragalin, Matematicheskii intuitsionizm: vvedenie v teoriyu dokazatelstv, Nauka, M., 1979 | MR | Zbl

[15] A. G. Dragalin, “Complete Heyting and Boolean algebras over a partial orderings. Constructive approach”, Konstruktivnaya teoriya dokazatelstv i nestandartnyi analiz, Editorial URSS, M., 2003, 398–453 | MR

[16] M. Kaminski, “Nonstandard connectives for intuitionistic propositional logic”, Notre Dame J. Formal Logic, 29:3 (1988), 309–331 | DOI | MR | Zbl