{"title":"Non-deterministic Connectives in Propositional Godel Logic","authors":"O. Lahav, A. Avron","doi":"10.2991/eusflat.2011.87","DOIUrl":null,"url":null,"abstract":"We define the notion of a canonical Godel system in the framework of single-conclusion hypersequent calculi. A corresponding general (nondeterministic) Godel valuation semantics is developed, as well as a (non-deterministic) linear intuitionistic Kripke-frames semantics. We show that every canonical Godel system induces a class of Godel 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 Godel logic.","PeriodicalId":403191,"journal":{"name":"EUSFLAT Conf.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EUSFLAT Conf.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2991/eusflat.2011.87","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We define the notion of a canonical Godel system in the framework of single-conclusion hypersequent calculi. A corresponding general (nondeterministic) Godel valuation semantics is developed, as well as a (non-deterministic) linear intuitionistic Kripke-frames semantics. We show that every canonical Godel system induces a class of Godel 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 Godel logic.