Non-deterministic Connectives in Propositional Gödel Logic
- 10.2991/eusflat.2011.87How to use a DOI?
- Propositional Gödel Logic, Nondeterministic Semantics, Hypersequent Calculi
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.
- © 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/).
Cite this article
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 -