{"title":"Exact Truthmaker Semantics for Modal Logics","authors":"Dongwoo Kim","doi":"10.1007/s10992-024-09752-9","DOIUrl":null,"url":null,"abstract":"<p>The present paper attempts to provide an exact truthmaker semantical analysis of modalized propositions. According to the present proposal, an exact truthmaker for “Necessarily <i>P</i>” is a state that bans every exact truthmaker for “Not <i>P</i>”, and an exact truthmaker for “Possibly <i>P</i>” is a state that allows an exact truthmaker for <i>P</i>. Based on this proposal, a formal semantics will be developed; and the soundness and completeness results for a well-known family of the systems of normal modal propositional logic will be established. It shall be seen that the present analysis offers an exactification of the standard Kripke semantics in the sense that it analyzes the accessibility relation between possible worlds in terms of the banning and allowing relations between the constituent states, and thereby gives an account of “truth at a possible world” in terms of exact truthmaking.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"64 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-04-04","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/s10992-024-09752-9","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
The present paper attempts to provide an exact truthmaker semantical analysis of modalized propositions. According to the present proposal, an exact truthmaker for “Necessarily P” is a state that bans every exact truthmaker for “Not P”, and an exact truthmaker for “Possibly P” is a state that allows an exact truthmaker for P. Based on this proposal, a formal semantics will be developed; and the soundness and completeness results for a well-known family of the systems of normal modal propositional logic will be established. It shall be seen that the present analysis offers an exactification of the standard Kripke semantics in the sense that it analyzes the accessibility relation between possible worlds in terms of the banning and allowing relations between the constituent states, and thereby gives an account of “truth at a possible world” in terms of exact truthmaking.
本文试图为模态化命题提供一种精确真值器语义分析。根据本提议，"必然 P "的精确造真符是一种禁止 "非 P "的每一个精确造真符的状态，而 "可能 P "的精确造真符是一种允许 P 的精确造真符的状态。根据本提议，将发展一种形式语义学；并将建立一个众所周知的正常模态命题逻辑系统族的健全性和完备性结果。我们将看到，目前的分析提供了标准克里普克语义学的精确化，因为它从组成状态之间的禁止和允许关系的角度分析了可能世界之间的可达性关系，从而从精确真值制造的角度给出了 "可能世界的真值 "的解释。
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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