Journal of Symbolic Logic

Interpolation for first order $S5$

Melvin Fitting

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An interpolation theorem holds for many standard modal logics, but first order $S5$ is a prominent example of a logic for which it fails. In this paper it is shown that a first order $S5$ interpolation theorem can be proved provided the logic is extended to contain propositional quantifiers. A proper statement of the result involves some subtleties, but this is the essence of it.

Article information

J. Symbolic Logic, Volume 67, Issue 2 (2002), 621-634.

First available in Project Euclid: 18 September 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}


Fitting, Melvin. Interpolation for first order $S5$. J. Symbolic Logic 67 (2002), no. 2, 621--634. doi:10.2178/jsl/1190150101.

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