{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T18:20:25Z","timestamp":1770747625211,"version":"3.49.0"},"reference-count":23,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2015,9,23]],"date-time":"2015-09-23T00:00:00Z","timestamp":1442966400000},"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":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2015,9,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    This article will introduce\n                    <jats:italic>K<\/jats:italic>\n                    -modal\n                    <jats:italic>BL<\/jats:italic>\n                    -logic and investigate some properties of this new logic. Consequently,\n                    <jats:italic>T<\/jats:italic>\n                    -modal\n                    <jats:italic>BL<\/jats:italic>\n                    -logic and\n                    <jats:italic>S<\/jats:italic>\n                    4-modal\n                    <jats:italic>BL<\/jats:italic>\n                    -logic, as schematic extensions of\n                    <jats:italic>K<\/jats:italic>\n                    -modal\n                    <jats:italic>BL<\/jats:italic>\n                    -logic, will be dealt with. Likewise, the algebraic semantics based on each logic will be constructed. Finally, the soundness and completeness theorems of these logics will be proved.\n                  <\/jats:p>","DOI":"10.3233\/ifs-151604","type":"journal-article","created":{"date-parts":[[2015,10,6]],"date-time":"2015-10-06T12:01:23Z","timestamp":1444132883000},"page":"377-388","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["On\n                    <i>K<\/i>\n                    -modal\n                    <i>BL<\/i>\n                    -logics"],"prefix":"10.1177","volume":"29","author":[{"given":"Esfandiar","family":"Eslami","sequence":"first","affiliation":[{"name":"Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran"}]},{"given":"Omid","family":"Yousefi Kia","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran"}]},{"given":"Arsham","family":"Borumand Saeid","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran"}]}],"member":"179","published-online":{"date-parts":[[2015,9,23]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-131002"},{"key":"e_1_3_2_3_2","first-page":"1","author":"Abramsky S","year":"1992","unstructured":"AbramskySGabbayDMMaibaumTSE1992Handbook of Logic in Computer Science, Clarendon Press-Oxford13","journal-title":"Handbook of Logic in Computer Science, Clarendon Press-Oxford"},{"key":"e_1_3_2_4_2","article-title":"Fuzzy equational logic","volume":"186","author":"Belohlavek R","year":"2005","unstructured":"BelohlavekRVychodilV2005Fuzzy equational logicStudies in Fuzziness and Soft Computing186","journal-title":"Studies in Fuzziness and Soft Computing"},{"issue":"2014","key":"e_1_3_2_5_2","first-page":"1371","article-title":"Implication BL-algebras","volume":"26","author":"Borumand Saeid A","unstructured":"Borumand SaeidAMohtashamniaNImplication BL-algebrasJ of Intelligent and Fuzzy Systems26201413711381","journal-title":"J of Intelligent and Fuzzy Systems"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0888-613X(98)00007-3"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.3233\/FI-1991-153-404"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.3233\/FI-1992-171-205"},{"key":"e_1_3_2_9_2","unstructured":"MelvinFRichardLM1998First-order modal logicKluwer Academic Publisher"},{"key":"e_1_3_2_10_2","article-title":"Many-dimensional modal logics","volume":"148","author":"Gabbay DM","year":"2003","unstructured":"GabbayDMKuruczAWolterFZakharyaschevM2003Many-dimensional modal logicsTheory and Applications, Elsevier Science BV148","journal-title":"Theory and Applications, Elsevier Science BV"},{"key":"e_1_3_2_11_2","unstructured":"GabbayDMHoggerCJRobinsonJA1994Handbook of Logic in Artificial Intelligence and LogicProgramming1-4Clarendon Press-Oxford"},{"key":"e_1_3_2_12_2","unstructured":"H\u00e1jekP1998Metamathematics of Fuzzy LogicKluwer Academic PublishersDordrecht"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2009.11.011"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.21136\/MB.2006.134083"},{"key":"e_1_3_2_15_2","unstructured":"HughesGECresswellMJ1996A New Introduction to Modal LogicLondon and New YorkRoutledge"},{"key":"e_1_3_2_16_2","unstructured":"IorgulescuA2008Algebras of logic as BCK algebrasBucharest University of EconomicsBucharest Romania"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.03.109"},{"key":"e_1_3_2_18_2","unstructured":"MossLSTiedeH-J2007Applications of Modal Logic in Linguistics Ch. 19BlackburnPVanBenthem JWolterF299341Handbook of Modal Logic Elsevier"},{"key":"e_1_3_2_19_2","first-page":"36","article-title":"Modalities in substructural logic- a preliminary report","author":"Ono H","year":"2005","unstructured":"OnoH2005Modalities in substructural logic- a preliminary reportProceedings of the 39th MLG meeting atGamagori3638Japan","journal-title":"Proceedings of the 39th MLG meeting atGamagori"},{"key":"e_1_3_2_20_2","first-page":"95","article-title":"Multiplier in BLalgebras","author":"Tayebi Khorami R","year":"2014","unstructured":"Tayebi KhoramiRBorumand SaeidA2014Multiplier in BLalgebrasIranian Journal of Science &Technology95103","journal-title":"Iranian Journal of Science &Technology"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370324"},{"key":"e_1_3_2_22_2","unstructured":"Yousefi KiaOEslamiEBorumand SaeidAK\u2013 modal BL\u2013 algebrassubmitted"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130847"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-008-0288-x"}],"container-title":["Journal of Intelligent &amp; 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