{"title":"Multiset-Multiset Frames","authors":"Takuro Onishi","doi":"10.1007/s10992-024-09764-5","DOIUrl":null,"url":null,"abstract":"<p>This paper presents the notion of <i>multiset-multiset frame</i> (mm-frame for short), a frame equipped with a relation between (finite) multisets over the set of points which satisfies the condition called <i>compositionality</i>. This notion is an extension of Restall and Standefer’s <i>multiset frame</i>, a frame that relates a multiset to a single point. While multiset frames serve as frames for the positive fragments of relevant logics <b>RW</b> and <b>R</b>, mm-frames are for the full <b>RW</b> and <b>R</b> with negation. We show this by presenting a way of constructing an mm-frame from any <i>GS</i>-frame, a frame with two dual ternary relations in which the Routley star is definable.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"2 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"JOURNAL OF PHILOSOPHICAL LOGIC","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s10992-024-09764-5","RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"0","JCRName":"PHILOSOPHY","Score":null,"Total":0}
引用次数: 0
Abstract
This paper presents the notion of multiset-multiset frame (mm-frame for short), a frame equipped with a relation between (finite) multisets over the set of points which satisfies the condition called compositionality. This notion is an extension of Restall and Standefer’s multiset frame, a frame that relates a multiset to a single point. While multiset frames serve as frames for the positive fragments of relevant logics RW and R, mm-frames are for the full RW and R with negation. We show this by presenting a way of constructing an mm-frame from any GS-frame, a frame with two dual ternary relations in which the Routley star is definable.
期刊介绍：
The Journal of Philosophical Logic aims to provide a forum for work at the crossroads of philosophy and logic, old and new, with contributions ranging from conceptual to technical. Accordingly, the Journal invites papers in all of the traditional areas of philosophical logic, including but not limited to: various versions of modal, temporal, epistemic, and deontic logic; constructive logics; relevance and other sub-classical logics; many-valued logics; logics of conditionals; quantum logic; decision theory, inductive logic, logics of belief change, and formal epistemology; defeasible and nonmonotonic logics; formal philosophy of language; vagueness; and theories of truth and validity. In addition to publishing papers on philosophical logic in this familiar sense of the term, the Journal also invites papers on extensions of logic to new areas of application, and on the philosophical issues to which these give rise. The Journal places a special emphasis on the applications of philosophical logic in other disciplines, not only in mathematics and the natural sciences but also, for example, in computer science, artificial intelligence, cognitive science, linguistics, jurisprudence, and the social sciences, such as economics, sociology, and political science.
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