Belief, knowledge and evidence

• URL: http://arxiv.org/abs/2304.01283v1
• Date: Mon, 3 Apr 2023 18:20:02 GMT
• Title: Belief, knowledge and evidence
• Abstract summary: We present a logical system that combines the well-known classical concepts of belief and knowledge with a concept of evidence. Inspired by citelewapal, we propose here a relational, frame-based semantics where belief and knowledge are not modeled via accessibility relations but directly as sets of propositions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a logical system that combines the well-known classical epistemic concepts of belief and knowledge with a concept of evidence such that the intuitive principle \textit{`evidence yields belief and knowledge'} is satisfied. Our approach relies on previous works of the first author \cite{lewjlc2, lewigpl, lewapal} who introduced a modal system containing $S5$-style principles for the reasoning about intutionistic truth (i.e. \textit{proof}) and, inspired by \cite{artpro}, combined that system with concepts of \textit{intuitionistic} belief and knowledge. We consider that combined system and replace the constructive concept of \textit{proof} with a classical notion of \textit{evidence}. This results in a logic that combines modal system $S5$ with classical epistemic principles where $\square\varphi$ reads as `$\varphi$ is evident' in an epistemic sense. Inspired by \cite{lewapal}, and in contrast to the usual possible worlds semantics found in the literature, we propose here a relational, frame-based semantics where belief and knowledge are not modeled via accessibility relations but directly as sets of propositions (sets of sets of worlds).

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