TY - GEN
T1 - A multiple-conclusion calculus for first-order Gödel logic
AU - Avron, Arnon
AU - Lahav, Ori
PY - 2011
Y1 - 2011
N2 - We present a multiple-conclusion hypersequent system for the standard first-order Gödel logic. We provide a constructive, direct, and simple proof of the completeness of the cut-free part of this system, thereby proving both completeness for its standard semantics, and the admissibility of the cut rule in the full system. The results also apply to derivations from assumptions (or non-logical axioms), showing that such derivations can be confined to those in which cuts are made only on formulas which occur in the assumptions. Finally, the results about the multiple-conclusion system are used to show that the usual single-conclusion system for the standard first-order Gödel logic also admits (strong) cut-admissibility.
AB - We present a multiple-conclusion hypersequent system for the standard first-order Gödel logic. We provide a constructive, direct, and simple proof of the completeness of the cut-free part of this system, thereby proving both completeness for its standard semantics, and the admissibility of the cut rule in the full system. The results also apply to derivations from assumptions (or non-logical axioms), showing that such derivations can be confined to those in which cuts are made only on formulas which occur in the assumptions. Finally, the results about the multiple-conclusion system are used to show that the usual single-conclusion system for the standard first-order Gödel logic also admits (strong) cut-admissibility.
UR - http://www.scopus.com/inward/record.url?scp=79959307138&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-20712-9_36
DO - 10.1007/978-3-642-20712-9_36
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AN - SCOPUS:79959307138
SN - 9783642207112
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 456
EP - 469
BT - Computer Science - Theory and Applications - 6th International Computer Science Symposium in Russia, CSR 2011, Proceedings
T2 - 6th International Computer Science Symposium in Russia, CSR 2011
Y2 - 14 June 2011 through 18 June 2011
ER -