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Uniform Interpolation and Propositional Quantifiers in Modal Logics

✍ Scribed by Marta Bílková

Publisher
Springer Netherlands
Year
2007
Tongue
English
Weight
291 KB
Volume
85
Category
Article
ISSN
0039-3215

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Quantiÿed hybrid logic is quantiÿed modal logic extended with apparatus for naming states and asserting that a formula is true at a named state. While interpolation and Beth's deÿnability theorem fail in a number of well-known quantiÿed modal logics (for example in quantiÿed modal K, T, D, S4, S4.3

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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.