Abstract

If Andrea knows that Biden won the last presidential election, then they also know that either Biden won the last presidential election, or Biden is a reptilian. This is the response that epistemic logics based on standard Kripke relational semantics provide, which is consistent with the fact that minimally rational agents can perform disjunction introduction. This is not the case in topic-sensitive semantics though. An agent might not grasp the concept of what a reptilian is, and therefore not be able to know any proposition dealing with reptilians. By employing the concept of logical grounding, I propose a semantics that keeps the requirement of topic-grasping but weakens it, re-establishing a more standard treatment of disjunction, in line with the capacities of minimally rational agents. The paper is structured as follows. In Section 2 I introduce topic-sensitive semantics. In Section 3 I introduce the concept of logical grounding – focusing on the grounds of disjunction – and motivate some desiderata. The concept of minimal topic, the core of my proposal, is detailed in Section 4 and exploited in Section 5 to propose a new topic-sensitive semantic clause for knowledge. I conclude in Section 6.