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title:
 
Non-deterministic Connectives in Propositional Gödel Logic
publication:
 
EUSFLAT
part of series:
  Advances in Intelligent Systems Research
volume-issue:   1 - 1
pages:   175 - 182
ISBN:
  978-90-78677-00-0
ISSN:
  1951-6851
DOI:
  doi:10.2991/eusflat.2011.87 (how to use a DOI)
author(s):
 
Ori Lahav, Arnon Avron
publication date:
 
July 2011
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:
 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/by-nc/4.0/
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