Relevant Reasoners in a Classical World

Igor Sedlár; Pietro Vigiani

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arXiv · 2206.03109

Relevant Reasoners in a Classical World

Igor Sedlár·Pietro Vigiani

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Abstract

We develop a framework for epistemic logic that combines relevant modal logic with classical propositional logic. In our framework the agent is modeled as reasoning in accordance with a relevant modal logic while the propositional fragment of our logics is classical. In order to achieve this feature, we modify the relational semantics for relevant modal logics so that validity in a model is defined as satisfaction throughout a set of designated states that, as far as propositional connectives are concerned, behave like classical possible worlds. The main technical result of the paper is a modular completeness theorem parametrized by the relevant modal logic formalizing the agent's reasoning.

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Igor Sedlár, Pietro Vigiani. 2022-06-07. Relevant Reasoners in a Classical World. https://arxiv.org/abs/2206.03109

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