{"metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00067109","sets":["934:935:936:5941"]},"path":["5941"],"owner":"10","recid":"67109","title":["Decidability and Undecidability Results of Modalμ-calculi with N∞ Semantics"],"pubdate":{"attribute_name":"公開日","attribute_value":"2009-11-20"},"_buckets":{"deposit":"17d5c4fc-8f62-41a8-bf75-d092e4eb624b"},"_deposit":{"id":"67109","pid":{"type":"depid","value":"67109","revision_id":0},"owners":[10],"status":"published","created_by":10},"item_title":"Decidability and Undecidability Results of Modalμ-calculi with N∞ Semantics","author_link":["0","0"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Decidability and Undecidability Results of Modalμ-calculi with N∞ Semantics"},{"subitem_title":"Decidability and Undecidability Results of Modalμ-calculi with N∞ Semantics","subitem_title_language":"en"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"発表概要","subitem_subject_scheme":"Other"}]},"item_type_id":"3","publish_date":"2009-11-20","item_3_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Ecole Normale Superieure"},{"subitem_text_value":"The University of Tokyo"},{"subitem_text_value":"The University of Tokyo"}]},"item_3_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Ecole Normale Superieure","subitem_text_language":"en"},{"subitem_text_value":"The University of Tokyo","subitem_text_language":"en"},{"subitem_text_value":"The University of Tokyo","subitem_text_language":"en"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_publisher":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"情報処理学会","subitem_publisher_language":"ja"}]},"publish_status":"0","weko_shared_id":-1,"item_file_price":{"attribute_name":"Billing file","attribute_type":"file","attribute_value_mlt":[{"url":{"url":"https://ipsj.ixsq.nii.ac.jp/record/67109/files/IPSJ-TPRO0205008.pdf"},"date":[{"dateType":"Available","dateValue":"2011-11-20"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-TPRO0205008.pdf","filesize":[{"value":"32.8 kB"}],"mimetype":"application/pdf","priceinfo":[{"tax":["include_tax"],"price":"0","billingrole":"5"},{"tax":["include_tax"],"price":"0","billingrole":"6"},{"tax":["include_tax"],"price":"0","billingrole":"15"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"052d0aec-a893-4825-bbe1-a7bf09d8c5e5","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2009 by the Information Processing Society of Japan"}]},"item_3_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Alexis, Goyet"},{"creatorName":"Masami, Hagiya"},{"creatorName":"Yoshinori, Tanabe"}],"nameIdentifiers":[{}]}]},"item_3_creator_6":{"attribute_name":"著者名(英)","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Alexis, Goyet","creatorNameLang":"en"},{"creatorName":"Masami, Hagiya","creatorNameLang":"en"},{"creatorName":"Yoshinori, Tanabe","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_3_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11464814","subitem_source_identifier_type":"NCID"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourceuri":"http://purl.org/coar/resource_type/c_6501","resourcetype":"journal article"}]},"item_3_source_id_11":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"1882-7802","subitem_source_identifier_type":"ISSN"}]},"item_3_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"In our previous study, we defined the semantics of modalμ-calculus on minplus algebra N∞and developed a model-checking algorithm. N∞is the set of all natural numbers and infinity (∞), and has two operations min and plus. In the semantics, disjunctions are interpreted by min and conjunctions by plus. This semantics allows interesting properties of a Kripke structure, such as the shortest path to some state or the number of states that satisfy a specified condition, to be expressed using simple formulae. In this study, we investigate the satisfiability problem in N∞semantics and prove decidability and undecidability results. First, the problem is decidable if the logic does not contain the implication operator. We prove this result by defining a translation tr(ψ) of formulaψsuch that the satisfiability ofψin N∞semantics is equivalent to that of tr(ψ) in ordinary semantics. Second, the satisfiablity problem becomes undecidable if the logic contains the implication operator.","subitem_description_type":"Other"}]},"item_3_description_8":{"attribute_name":"論文抄録(英)","attribute_value_mlt":[{"subitem_description":"In our previous study, we defined the semantics of modalμ-calculus on minplus algebra N∞and developed a model-checking algorithm. N∞is the set of all natural numbers and infinity (∞), and has two operations min and plus. In the semantics, disjunctions are interpreted by min and conjunctions by plus. This semantics allows interesting properties of a Kripke structure, such as the shortest path to some state or the number of states that satisfy a specified condition, to be expressed using simple formulae. In this study, we investigate the satisfiability problem in N∞semantics and prove decidability and undecidability results. First, the problem is decidable if the logic does not contain the implication operator. We prove this result by defining a translation tr(ψ) of formulaψsuch that the satisfiability ofψin N∞semantics is equivalent to that of tr(ψ) in ordinary semantics. Second, the satisfiablity problem becomes undecidable if the logic contains the implication operator.","subitem_description_type":"Other"}]},"item_3_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"46","bibliographic_titles":[{"bibliographic_title":"情報処理学会論文誌プログラミング（PRO）"}],"bibliographicPageStart":"46","bibliographicIssueDates":{"bibliographicIssueDate":"2009-11-20","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"5","bibliographicVolumeNumber":"2"}]},"relation_version_is_last":true,"weko_creator_id":"10"},"updated":"2025-01-22T00:44:28.402189+00:00","created":"2025-01-18T23:27:39.986096+00:00","links":{},"id":67109}