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ALGEBRAIC SEMANTICS FOR RELATIVE TRUTH, AWARENESS, AND POSSIBILITY

Part of: General logic Algebraic logic

Published online by Cambridge University Press:  28 September 2023

EVAN PIERMONT Open the ORCID record for EVAN PIERMONT [Opens in a new window]
EVAN PIERMONT*
Affiliation:
DEPARTMENT OF ECONOMICS ROYAL HOLLOWAY UNIVERSITY OF LONDON EGHAM TW20 0EX, UK
*
E-mail: evan.piermont@rhul.ac.uk
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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.

Keywords

relativized Boolean algebrasawareness framesawareness logics

MSC classification

Primary: 03B42: Logics of knowledge and belief (including belief change) 03G27: Abstract algebraic logic 06E25: Boolean algebras with additional operations (diagonalizable algebras, etc.)

Information

Type
Research Article
Information
The Review of Symbolic Logic , Volume 17 , Issue 1 , March 2024 , pp. 154 - 177
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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