{"title":"The Craig interpolation property in first-order Gödel logic","authors":"N.R. Tavana , M. Pourmahdian , S.M.A. Khatami","doi":"10.1016/j.fss.2024.108958","DOIUrl":null,"url":null,"abstract":"<div><p>In this article, a model-theoretic approach is proposed to prove that the first-order Gödel logic, <strong>G</strong>, as well as its extension <span><math><msup><mrow><mi>G</mi></mrow><mrow><mi>Δ</mi></mrow></msup></math></span> associated with first-order relational languages enjoy the Craig interpolation property. These results partially provide an affirmative answer to a question posed in <span>[1]</span>.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Sets and Systems","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165011424001040","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, a model-theoretic approach is proposed to prove that the first-order Gödel logic, G, as well as its extension associated with first-order relational languages enjoy the Craig interpolation property. These results partially provide an affirmative answer to a question posed in [1].
期刊介绍：
Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies.
In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.
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