{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T04:10:49Z","timestamp":1751429449158,"version":"3.41.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2014,11]]},"abstract":"<jats:p> To model and analyze systems with multi-valued information, in this paper, we present an extension of Kripke structures in the framework of complete residuted lattices, which we will refer to as lattice-valued Kripke structures (LKSs). We then show how the traditional trace containment and equivalence relations, can be lifted to the lattice-valued setting, and we introduce two families of lattice-valued versions of the relations. Further, we explore some interesting properties of these relations. Finally, we provide logical characterizations of our relations by a natural extension of linear temporal logic. <\/jats:p>","DOI":"10.3233\/fi-2014-1122","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T06:18:38Z","timestamp":1575353918000},"page":"269-293","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":8,"title":["Quantitative Analysis of Lattice-valued Kripke Structures"],"prefix":"10.1177","volume":"135","author":[{"given":"Haiyu","family":"Pan","sequence":"first","affiliation":[{"name":"College of Computer Science, Shaanxi Normal University, Xi'an 710062, China. phyu76@126.com"}]},{"given":"Min","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, 200062, Shanghai, China. mzhang@sei.ecnu.edu.cn"}]},{"given":"Hengyang","family":"Wu","sequence":"additional","affiliation":[{"name":"Information Engineer College, Hangzhou Dianzi University, 310018, Hangzhou, China. wuhengy_1974@aliyun.com"}]},{"given":"Yixiang","family":"Chen","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, 200062, Shanghai, China. yxchen@sei.ecnu.edu.cn"}]}],"member":"179","published-online":{"date-parts":[[2014,1,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2014-1122","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2014-1122","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:50:01Z","timestamp":1751367001000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2014-1122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,1]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,11]]}},"alternative-id":["10.3233\/FI-2014-1122"],"URL":"https:\/\/doi.org\/10.3233\/fi-2014-1122","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"type":"print","value":"0169-2968"},{"type":"electronic","value":"1875-8681"}],"subject":[],"published":{"date-parts":[[2014,1,1]]}}}