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<p>We introduce a dynamic extension of the logic of relevant reasoners in classical worlds, where dynamic modalities model the update of agents’ beliefs. We argue that the system can be used to define a binary relative necessity operator, in the style of conditional logics, which captures Ramsey’s idea that conditional reasoning involves a form of belief revision. Recast as a relevant conditional logic, the system combines the best of existing classical and relevant conditional logics: it extends classical propositional logic, while adopting relevant implication to formalise the non-monotonic aspects of belief revision. The main technical result of the paper is a sound and complete axiomatisation of the logic and its extensions with respect to neighborhood Routley–Meyer models for dynamic relevant modal logic, enriched with possible worlds.</p>

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Ramsey Conditionals in Dynamic Relevant Logic

  • 期刊论文

  • 发表日期：

    2025年12月4日

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  • Pietro Vigiani

摘要

We introduce a dynamic extension of the logic of relevant reasoners in classical worlds, where dynamic modalities model the update of agents’ beliefs. We argue that the system can be used to define a binary relative necessity operator, in the style of conditional logics, which captures Ramsey’s idea that conditional reasoning involves a form of belief revision. Recast as a relevant conditional logic, the system combines the best of existing classical and relevant conditional logics: it extends classical propositional logic, while adopting relevant implication to formalise the non-monotonic aspects of belief revision. The main technical result of the paper is a sound and complete axiomatisation of the logic and its extensions with respect to neighborhood Routley–Meyer models for dynamic relevant modal logic, enriched with possible worlds.