Reasoning with Relevant Epistemic Logics

The present dissertation investigates the relationships between classical and non-classical logics within a common logical platform, in which it is possible to address philosophical questions. More specifically, the focus of the dissertation lies in applications of relevant logics to problems in formal epistemology, such as the problem of logical omnisicence, the distinction between explicit and implicit beliefs, and the modeling of belief revision. As the main contribution of the present work, I devise so-called contextual modal logics, i.e. modal logics where modal operators individuate the range of application of a given logic, to be chosen from the class of extensions of weak relevant logics. In this way, I argue that it is possible to adequately formalise the context-sensitivity of reasoning, a feature which arises when we confront reasoning about the factual and the epistemic domain. Contextual modal logics are presented both semantically and proof-theoretically, by means of Hilbert-style axiom systems. The language of the logics is modularly extended, from the basic relevant language, so as to include topic sensitive operators, implicit belief operators and dynamic operators. Characterisation results are obtained for all extensions of the logics in the contextual modal family.