Abstract
This is a survey of results on interpolation in propositional normal modal logics. Interpolation properties of these logics are closely connected with amalgamation properties of varieties of modal algebras. Therefore, the results on interpolation are also reformulated in terms of amalgamation.
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References
P.D. Bacsich, Amalgamation properties and interpolation theorems for equational theories, Algebra Universalis 5, 1 (1975), pp. 44–55.
W. J. Blok, Pretabular varieties of modal algebras, Studia Logica 30, 2/3 (1980), pp. 101–124.
G. Boolos, On systems of modal logic with provability interpretations, Theoria 45, 1 (1980), pp. 7–18.
J. Czelakowski, Logical matrices and the amalgamation property, Studia Logica 41, 4 (1982), pp. 329–341.
K. Fine, Failures of the interpolation lemma in quantified modal logic, Journal of Symbolic Logic 44, 2 (1979), pp. 201–206.
D. Gabbay, Craig's interpolation theorem for modal logics, in Conference in Mathematical Logic — London '70 (1972), pp. 111–127, Springer, Berlin.
R. Goldblatt, Arithmetical necessity, provability and intuitionistic logic, Theoria 44 (1978), pp. 38–46.
S. Kripke, Semantical analysis of modal logic I. Normal modal propositional calculi, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 9 (1963), pp. 67–96.
A. V. Kuznetsov and A. Y. Muravitski, Provability as modality, (in Russian), in Aktualnye problemy logiki i metodologii nauki (1980), pp. 193–229, Naukova dumka, Kyev.
E. Lemmon, Algebraic semantics for modal logics. I, Journal of Symbolic Logic 31 (1966), pp. 46–65. II, Journal of Symbolic Logic, 31 (1966), pp. 191–218
D. Makinson, On some completeness theorems in modal logic, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 12 (1966), pp. 379–384.
L. L. Maksimova, On a classification of modal logics, (in Russian), Algebra i logika 18, 3 (1979), pp. 328–340.
L. L. Maksimova, Interpolation theorems in modal logics and amalgamated varieties of topoboolean algebras, (in Russian), Algebra i logika 18, 5 (1979), pp. 556–586.
L. L. Maksimova, Interpolation theorems in modal logics. Sufficient conditions, (in Russian), Algebra i logika 19, 2 (1980), pp. 194–213.
L. L. Maksimova, Failure of interpolation property in modal counterparts of Dummett's logic, (in Russian), Algebra i logika 21, 6 (1982), pp. 690–694.
L. L. Maksimova, Lyndon's interpolation theorem in modal logics, in Matematicheskaya logika i teoria algoritmov (1982), pp. 84–87, Nauka (Siberian Division), Novosibirsk.
L. L. Maksimova, Interpolation properties of superintuitionistic, positive and modal logics, in Intensional Logics: Theory and Applications (V. 35, 1982), pp. 70–78, Acta Philosophica Fennica, Helsinki.
L. L. Maksimova, On interpolation in modal logics containing S4, 7th International Congress of Logic, Methodology and Philosophy of Science, Salzburg, 1983, Abstracts 1, pp. 84–87.
L. L. Maksimova, On the number of amalgamated varieties of topoboolean algebras, (in Russian), 17 Vsesoyuznaya algebraicheskaya konferencya, tezytsy, part 2, Minsk, 1983, pp. 135–136.
L. L. Maksimova, On interpolation in normal modal logics, (in Russian), in Neklassicheskie logiki (1987), pp. 40–56, Stiinca, Kishinev.
L. L. Maksimova, Interpolation in modal logics of infinite slice containing K4, (in Russian), in Matematicheskaya logika i algorithmicheskie problemy (1989), Nauka (Siberian Division), Novosibirsk.
L. L. Maksimova, Interpolation in infinite-slice extensions of the provability logic, (in Russian), Algebra i logika 27, 5 (1988), pp. 581–604.
V. Y. Meschi, Algebraic analysis of modal fragments of tense logics, (in Russian), in Logika, semantika, metodologia (1978), pp. 113–124, Metsniereba, Tbilissi.
D. Pigozzi, Amalgamation, congruence extension and interpolation properties in algebras, Algebra Universalis 1/3 (1972), pp. 269–349.
W. Rautenberg, Modal tableau calculi and interpolation, Journal of Philosophical Logic 12 (1983), pp. 403–423.
G. Schumm, Interpolation in S5 and related systems, Reports on Mathematical Logic 6 (1976), pp. 107–110.
K. Segerberg, An Essay in Classical Modal Logic (1971), Uppsala.
C. Smorynski, Beth's theorem and self-referential sentences, in Logic Colloquium '77 (pp. 253–261), North-Holland, Amsterdam.
S. K. Thomason, Categories of frames for modal logic, Journal of Symbolic Logic 40, 3 (1975), pp. 439–442.
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Maksimova, L. Amalgamation and interpolation in normal modal logics. Stud Logica 50, 457–471 (1991). https://doi.org/10.1007/BF00370682
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DOI: https://doi.org/10.1007/BF00370682