title: |
Non-deterministic Connectives in Propositional Gpdel Logic |
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publication: |
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part of series: |
Advances in Intelligent Systems Research | |
| pages: | 175 - 182 | |
DOI: |
To be assigned soon (how to use a DOI) | |
author(s): |
Ori Lahav, Arnon Avron |
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publication date: |
July 2011 |
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keywords: |
Propositional Gödel Logic, Nondeterministic Semantics, Hypersequent Calculi |
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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. |
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |