Marko Stanković , Stefan Stanimirović , Miroslav Ćirić
{"title":"Heyting代数上模糊多模态逻辑的近似Hennessy-Milner型定理","authors":"Marko Stanković , Stefan Stanimirović , Miroslav Ćirić","doi":"10.1016/j.ijar.2025.109362","DOIUrl":null,"url":null,"abstract":"<div><div>In the present paper, we introduce <em>λ</em>-approximate weak simulations and bisimulations on a given set of modal formulae between two fuzzy Kripke models of fuzzy multimodal logics. The parameter <em>λ</em>, which is an element from the linearly ordered Heyting algebra, is used to quantify the approximation degree of modal equivalence between the two worlds from the different models, with respect to the given set of formulae, within the framework of linearly ordered Heyting algebras. In a recent paper, we introduced <em>λ</em>-approximate simulations and bisimulations between fuzzy Kripke models. This paper investigates the relationships between <em>λ</em>-approximate bisimulations and <em>λ</em>-approximate weak bisimulations, yielding three Approximate Hennessy-Milner Type Theorems. We also provide an algorithm that divides the real unit interval into subintervals with the same degree of modal equivalence for two given fuzzy Kripke models. Moreover, we extend the Approximate Hennessy-Milner Type Theorems to the class of witnessed and modally saturated fuzzy Kripke models.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"179 ","pages":"Article 109362"},"PeriodicalIF":3.0000,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximate Hennessy-Milner type theorems for fuzzy multimodal logics over Heyting algebras\",\"authors\":\"Marko Stanković , Stefan Stanimirović , Miroslav Ćirić\",\"doi\":\"10.1016/j.ijar.2025.109362\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In the present paper, we introduce <em>λ</em>-approximate weak simulations and bisimulations on a given set of modal formulae between two fuzzy Kripke models of fuzzy multimodal logics. The parameter <em>λ</em>, which is an element from the linearly ordered Heyting algebra, is used to quantify the approximation degree of modal equivalence between the two worlds from the different models, with respect to the given set of formulae, within the framework of linearly ordered Heyting algebras. In a recent paper, we introduced <em>λ</em>-approximate simulations and bisimulations between fuzzy Kripke models. This paper investigates the relationships between <em>λ</em>-approximate bisimulations and <em>λ</em>-approximate weak bisimulations, yielding three Approximate Hennessy-Milner Type Theorems. We also provide an algorithm that divides the real unit interval into subintervals with the same degree of modal equivalence for two given fuzzy Kripke models. Moreover, we extend the Approximate Hennessy-Milner Type Theorems to the class of witnessed and modally saturated fuzzy Kripke models.</div></div>\",\"PeriodicalId\":13842,\"journal\":{\"name\":\"International Journal of Approximate Reasoning\",\"volume\":\"179 \",\"pages\":\"Article 109362\"},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2025-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Approximate Reasoning\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0888613X25000039\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/1/15 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Approximate Reasoning","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0888613X25000039","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/15 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
Approximate Hennessy-Milner type theorems for fuzzy multimodal logics over Heyting algebras
In the present paper, we introduce λ-approximate weak simulations and bisimulations on a given set of modal formulae between two fuzzy Kripke models of fuzzy multimodal logics. The parameter λ, which is an element from the linearly ordered Heyting algebra, is used to quantify the approximation degree of modal equivalence between the two worlds from the different models, with respect to the given set of formulae, within the framework of linearly ordered Heyting algebras. In a recent paper, we introduced λ-approximate simulations and bisimulations between fuzzy Kripke models. This paper investigates the relationships between λ-approximate bisimulations and λ-approximate weak bisimulations, yielding three Approximate Hennessy-Milner Type Theorems. We also provide an algorithm that divides the real unit interval into subintervals with the same degree of modal equivalence for two given fuzzy Kripke models. Moreover, we extend the Approximate Hennessy-Milner Type Theorems to the class of witnessed and modally saturated fuzzy Kripke models.
期刊介绍：
The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest.
Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning.
Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
