Logical Omniscience as a Conditionality Issue. A Multi-Modal Approach

Many solutions to the problem of Logical Omniscience assume that this arises from the behavior of the epistemic operators. However, few proposals have criticized the assumption that material implication accurately accounts for conditionality. This paper aims to show how Multi-Modal Logic can be used to criticize this assumption. After reviewing a kind of fusion semantics that incorporates a set of epistemic states to the models, serious systems of Multi-Modal Logic are used to criticize both the validity of Closure Principles for Knowledge and Belief and a version of Logical Omniscience that uses the strict conditional. The machinery is also modified to explore Logical Omniscience in logics based on Conditional Logic, Intuitionistic Logic, and a pair of weak Relevant Logics.