Non-deterministic Connectives in Propositional Gödel Logic

DOI

10.2991/eusflat.2011.87How to use a DOI?

Keywords

Propositional Gödel Logic, Nondeterministic Semantics, Hypersequent Calculi

Abstract

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.

Copyright

© 2011, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Ori Lahav
AU  - Arnon Avron
PY  - 2011/08
DA  - 2011/08
TI  - Non-deterministic Connectives in Propositional Gödel Logic
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)
PB  - Atlantis Press
SP  - 175
EP  - 182
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.87
DO  - 10.2991/eusflat.2011.87
ID  - Lahav2011/08
ER  -