<p>This paper sets out to extend the epistemic semantics presented in Dahl (<CitationRef CitationID="CR9">2023</CitationRef>)&#xa0;to modal and conditional logics. To do so, I extend the notion of belief expansion systems, inspired by the AGM-model of belief change, to include <i>belief revision</i>, and use the resulting structures as models for both conditional and modal logic. In the first case, this applies the well-known approach to conditionals initiated by Gärdenfors (<CitationRef CitationID="CR13">1978</CitationRef>), but in a weaker setting which doesn’t assume an underlying logic. As such, we get semantics for both classical conditional logic and the intuitionistic conditionals studied by Weiss (<CitationRef CitationID="CR27">2019</CitationRef>). For modal logics, I use the condition that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Box \varphi\)</EquationSource> </InlineEquation> is accepted if and only if <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varphi\)</EquationSource> </InlineEquation> is accepted under every belief revision. As a result of this system of semantics, we get soundness and completeness theorems for both classical and non-classical systems of modal and conditional logic on the basis of a single type of structure. Finally, I briefly discuss how models based on belief change can still be thought to explain the semantics of objective modal claims.</p>

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From belief change to modality: Epistemic semantics for modal and conditional logic

  • Niklas Dahl

摘要

This paper sets out to extend the epistemic semantics presented in Dahl (2023) to modal and conditional logics. To do so, I extend the notion of belief expansion systems, inspired by the AGM-model of belief change, to include belief revision, and use the resulting structures as models for both conditional and modal logic. In the first case, this applies the well-known approach to conditionals initiated by Gärdenfors (1978), but in a weaker setting which doesn’t assume an underlying logic. As such, we get semantics for both classical conditional logic and the intuitionistic conditionals studied by Weiss (2019). For modal logics, I use the condition that \(\Box \varphi\) is accepted if and only if \(\varphi\) is accepted under every belief revision. As a result of this system of semantics, we get soundness and completeness theorems for both classical and non-classical systems of modal and conditional logic on the basis of a single type of structure. Finally, I briefly discuss how models based on belief change can still be thought to explain the semantics of objective modal claims.