TY - GEN
T1 - Non-deterministic Connectives in Propositional Gödel Logic
AU - Lahav, Ori
AU - Avron, Arnon
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Hypersequent Calculi
KW - Nondeterministic Semantics
KW - Propositional Gödel Logic
UR - http://www.scopus.com/inward/record.url?scp=84872162054&partnerID=8YFLogxK
U2 - 10.2991/eusflat.2011.87
DO - 10.2991/eusflat.2011.87
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AN - SCOPUS:84872162054
SN - 9789078677000
T3 - Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2011 and French Days on Fuzzy Logic and Applications, LFA 2011
SP - 175
EP - 182
BT - Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2011 and French Days on Fuzzy Logic and Applications, LFA 2011
T2 - Joint 7th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2011 and 17th French Days on Fuzzy Logic and Applications, LFA 2011
Y2 - 18 July 2011 through 18 July 2011
ER -