Non-deterministic Connectives in Propositional Godel Logic
نویسندگان
چکیده
We define the notion of a canonical Gödel system in the framework of single-conclusion hypersequent calculi. A corresponding general (nondeterministic) Gödel valuation semantics is developed, as well as a (non-deterministic) linear intuitionistic Kripke-frames semantics. We show that every canonical Gödel system induces a class of Gödel valuations (and of Kripke frames) for which it is strongly sound and complete. The semantics is used to identify the canonical systems that enjoy (strong) cut-admissibility, and to provide a decision procedure for these systems. The results of this paper characterize, both proof-theoretically and semantically, a large family of (non-deterministic) connectives that can be added to propositional Gödel logic.
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