Amalgamation and interpolation in normal modal logics

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.

[1]  P. Bacsich.  Amalgamation properties and interpolation theorems for equational theories , 1975 .

[2]  Wolfgang Rautenberg,et al.  Modal tableau calculi and interpolation , 1983, J. Philos. Log..

[3]  J. Czelakowski.  Logical matrices and the amalgamation property , 1982 .

[4]  E. J. Lemmon,et al.  Algebraic semantics for modal logics I , 1966, Journal of Symbolic Logic (JSL).

[5]  L. L. Maksimova.  Absence of the interpolation property in the consistent normal modal extensions of the dummett logic , 1982 .

[6]  Steven K. Thomason.  Categories of Frames for Modal Logic , 1975, J. Symb. Log..

[7]  Saul A. Kripke,et al.  Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi , 1963 .

[8]  L. Maksimova.  Interpolation theorems in modal logics and amalgamable varieties of topological Boolean algebras , 1979 .

[9]  D. Makinson.  On Some Completeness Theorems in Modal Logic , 1966 .

[10]  Craig Smorynski,et al.  Beth's Theorem and Self-Referential Sentences , 1978 .

[11]  L. Maksimova.  Interpolation theorems in modal logics. Sufficient conditions , 1980 .

[12]  C. Smoryński,et al.  Provability as Modality , 1985 .

[13]  Kit Fine,et al.  Failures of the interpolation lemma in quantified modal logic , 1979, Journal of Symbolic Logic.

[14]  Krister Segerberg,et al.  An essay in classical modal logic , 1971 .

[15]  Don Pigozzi,et al.  Amalgamation, congruence-extension, and interpolation properties in algebras , 1971 .

[16]  L. L. Maksimova,et al.  A classification of modal logics , 1979 .

[17]  D. Gabbay.  Craig's interpolation theorem for modal logics , 1972 .

[18]  W. J. Blok,et al.  Pretabular varieties of modal algebras , 1980 .

[19]  Interpolation in infinitely layered extensions of provability logic , 1988 .