A multiple-conclusion calculus for first-order Gödel logic

Arnon Avron*, Ori Lahav

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publicationComputer Science - Theory and Applications - 6th International Computer Science Symposium in Russia, CSR 2011, Proceedings
Pages456-469
Number of pages14
DOIs
StatePublished - 2011
Event6th International Computer Science Symposium in Russia, CSR 2011 - St. Petersburg, Russian Federation
Duration: 14 Jun 201118 Jun 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6651 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference6th International Computer Science Symposium in Russia, CSR 2011
Country/TerritoryRussian Federation
CitySt. Petersburg
Period14/06/1118/06/11

Fingerprint

Dive into the research topics of 'A multiple-conclusion calculus for first-order Gödel logic'. Together they form a unique fingerprint.

Cite this