{"title":"ALGEBRAIC SEMANTICS FOR RELATIVE TRUTH, AWARENESS, AND POSSIBILITY","authors":"Evan Piermont","doi":"10.1017/s1755020323000308","DOIUrl":null,"url":null,"abstract":"Abstract This paper puts forth a class of algebraic structures, relativized Boolean algebras (RBAs), that provide semantics for propositional logic in which truth/validity is only defined relative to a local domain. In particular, the join of an event and its complement need not be the top element. Nonetheless, behavior is locally governed by the laws of propositional logic. By further endowing these structures with operators—akin to the theory of modal Algebras—RBAs serve as models of modal logics in which truth is relative. In particular, modal RBAs provide semantics for various well-known awareness logics and an alternative view of possibility semantics.","PeriodicalId":49628,"journal":{"name":"Review of Symbolic Logic","volume":"5 1","pages":"0"},"PeriodicalIF":0.9000,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Review of Symbolic Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s1755020323000308","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract This paper puts forth a class of algebraic structures, relativized Boolean algebras (RBAs), that provide semantics for propositional logic in which truth/validity is only defined relative to a local domain. In particular, the join of an event and its complement need not be the top element. Nonetheless, behavior is locally governed by the laws of propositional logic. By further endowing these structures with operators—akin to the theory of modal Algebras—RBAs serve as models of modal logics in which truth is relative. In particular, modal RBAs provide semantics for various well-known awareness logics and an alternative view of possibility semantics.
期刊介绍：
The Review of Symbolic Logic is designed to cultivate research on the borders of logic, philosophy, and the sciences, and to support substantive interactions between these disciplines. The journal welcomes submissions in any of the following areas, broadly construed:
- The general study of logical systems and their semantics,including non-classical logics and algebraic logic;
- Philosophical logic and formal epistemology, including interactions with decision theory and game theory;
- The history, philosophy, and methodology of logic and mathematics, including the history of philosophy of logic and mathematics;
- Applications of logic to the sciences, such as computer science, cognitive science, and linguistics; and logical results addressing foundational issues in the sciences.
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