Fixed-Point Logic with the Approximation Modality and Its Kripke Completeness

Authors:
Hiroshi Nakano
Affiliations:
-
Venue:
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
Year:
2001

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Abstract

We present two modal typing systems with the approximation modality, which has been proposed by the author to capture selfreferences involved in computer programs and their specifications. The systems are based on the simple and the F-semantics of types, respectively, and correspond to the same modal logic, which is considered the intuitionistic version of the logic of provability. We also show Kripke completeness of the modal logic and its decidability, which implies the decidability of type inhabitance in the typing systems.