AAP 2026 CONFERENCE

Recent years have seen growing interest in applying relevant logics to formal epistemology. These logics, with their relational semantics, offer a natural framework for modelling agents with incomplete or inconsistent information, while avoiding problematic classical results such as paradoxes of material implication. When epistemic operators are added to relevant logics, we obtain systems where agents need not possess the full rational powers assumed in classical epistemic logic—for instance, agents may not know all valid formulas. However, even these systems retain a strong idealization: agents remain closed under relevant logical consequence, knowing all relevant consequences of their knowledge. This talk proposes an alternative approach: a relevant epistemic logic that imposes only a weak, minimal rationality constraint to agents. In this system, agents’ knowledge is not closed under all relevant consequences, thereby allowing for failures of deductive reasoning even within the framework of relevant logic. The aim is to better capture the topicality constraints and cognitive limitations that real agents face. I will outline the formal properties of this system and discuss its philosophical implications for the study of knowledge and rationality.