This is a preview of subscription content, log in via an institution to check access.
Literature cited
L. L. Maksimova, "Pretabular extensions of the logic S4 of Lewis," Algebra Logika,14, No. 1, 28–55 (1975).
L. Esakia and V. Meskhi, "Five critical modal system," Theoria,43, 52–60 (1977).
L. L. Esakia, "On the variety of Grzegorczyk's algebras," in: Studies on Nonclassical Logics and Set Theory [in Russian], Nauka, Moscow (1979), pp. 257–287.
L. L. Maksimova, "Craig's theorem in superintuitionistic logics and amalgamated varieties of pseudo-Boolean algebras," Algebra Logika,16, No. 6, 643–681 (1977).
L. L. Maksimova, "Interpolation theorems in modal logics and amalgamated varieties of topo-Boolean algebras," Algebra Logika,18, No. 5, 556–586 (1979).
A. V. Chagrov, "Superintuitionistic fragments of abnormal modal logics," in: Mathematical Logic and Mathematical Linguistics [in Russian], Kalinin (1981), pp. 144–162.
A. V. Chagrov, "On abnormal modal counterparts of Int," in: Automata, Algorithms, Languages [in Russian], Kalinin (1982), pp. 133–148.
A. G. Dragalin, Mathematical Intuitionism, Introduction to Proof Theory [in Russian], Nauka, Moscow (1979).
D. Vakarelov, "Intuitionistic modal logics incompatible with the law of the excluded middle," Stud. Logica,40, No. 2, 103–111 (1981).
B. Jónsson and A. Tarski, "Boolean algebras with operators," Am. J. Math.,73, No. 4, 891–939 (1951).
E. Rasiowa and R. Sikorski, Mathematics of Metamathematics [Russian translation], Nauka, Moscow (1972).
A. I. Mal'tsev, Algebraic Systems [in Russian], Nauka, Moscow (1970).
R. V. Kohn, "Some Post-complete extensions of S2 and S3," Notre Dame J. Form. Log.,18, No. 3, 467–470 (1977).
H. Ohno, "Kripke models and intermediate logics," Publ. RIMS Kyoto Univ.,6, 467–476 (1970/71).
L. A. Chagrova, "Countability of the set of Post complete extensions of the modal logic S3," in: Automata, Algorithms, Languages [in Russian], Kalinin (1982), pp. 148–162.
G. Sambin and S. Valentini, "Post completeness and free algebras," Z. Math. Logik Grundlagen Math.,26, 343–347 (1980).
R. Solovay, "Provability interpretation of modal logic," Israel J. Math.,25, 287–304 (1976).
S. N. Artemov, "Arithmetically complete modal theories," in: Semiotics and Information [in Russian], Vol. 14 (1980), pp. 115–133.
G. Boolos, "On systems of modal logic with provability interpretations," Theoria,46, No. 1, 7–18 (1980).
K. Fine, "Logics containing K4," J. Symb. Logic,39, No. 1, 31–42 (1974).
S. K. Thomason, "Semantic analysis of tense logics," J. Symb. Logic,37, No. 1 (1972).
S. K. Thomason, "The logical consequence relation of propositional tense logic," Z. Math. Logik Grundl. Math.,21, 29–40 (1975).
V. B. Shekhtman, "On countable approximability of superintuitionistic and modal logics," in: Studies in Nonclassical Logics and Formal Systems [in Russian], Nauka, Moscow (1983), pp. 287–299.
W. Blok, Varieties of Interior Algebras, Dissertation, University of Amsterdam (1976).
J. C. C. McKinsey and A. Tarski, "Some theorems about the sentential calculi of Lewis and Heyting," J. Symb. Logic,13, 1–15 (1948).
P. S. Novikov, Constructive Mathematical Logic from the Classical Point of View [in Russian], Nauka, Moscow (1977).
A. V. Chagrov, "On minimal modal counterparts of Int," in: Semiotic Aspects of Formalization of Intellectual Activity (Seminar Telavi-83) [in Russian], Moscow (1983), pp. 138–140.
K. Segerberg, An Essay in Classical Modal Logic, Uppsala (1971).
K. Segerberg, "That every extension of S4.3 is normal," in: Proceedings of the Third Scandinavian Logic Symposium, Amsterdam (1975), pp. 194–196.
L. L. Maksimova, "Modal logics of finite layers," Algebra Logika,14, No. 3, 304–319 (1975).
Additional information
Translated from Algebra i Logika, Vol. 24, No. 4, pp. 426–489, July–August, 1985.
Rights and permissions
About this article
Cite this article
Chagrov, A.V. Varieties of logical matrices. Algebra and Logic 24, 278–325 (1985). https://doi.org/10.1007/BF01984693
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01984693