Improving the Agent’s Formalization of Relevance: An Epistemic Logic Grounded in Possible Knowledge Bases

When faced with complex epistemic-combinatorial situations, agents struggle to formally differentiate between relational patterns, creating gaps in formal models. To address this, we introduce strictly relevant operators (( \(\phi \ \vert \ \psi \) ), ( \(\phi \ \Vert \ \psi \) ), ( \(\phi \not \mid \psi \) )) and construct an Epistemic Logic based on Possible Knowledge Bases ( \(EL_{PKB}\) ). Among these, these new operators require not only the absence of counterexample situations but also every truth case must exist, ensuring a precise representation. To this end, we introduce a non-Kripke model that incorporates PKBs to define the semantics. In this context, a PKB refers to the knowledge combinations that an agent might possess in a given state. Then we explore the correspondence between PKBs and Global Modal Logic models within the proposed framework, while also providing variants of RN for \(EL_{PKB}\) . Finally, we also explore the cognitive attributes of agents, particularly focusing on two distinct levels of facticity and positive introspection within agent cognition. This capability to identify logical relevance is also a critical step toward enabling AI to approach human-level cognition.