One of the initial applications of modal logic was Hintikka’s [1962] logic of knowledge and belief. Utilizing Kripke frames, wherein each world is conceptualized as an epistemic state, an agent’s belief in a proposition is defined by its truth value across those epistemic states to which the agent has access. This approach facilitated the definition of related concepts, such as knowledge and epistemic possibility, thus establishing a promising area of research. 

Nevertheless, a persistent challenge emerged from this methodology: the issue of logical omniscience. For agents to be considered rational within such models, certain requirements are made; specifically, the acceptance of contradictions must be eschewed, and the application of modus ponens should be standardized. Consequently, if agents are modelled as rational according to these criteria, they are ipso facto logically omniscient: they possess complete awareness of the logical consequences of their beliefs and are aware of all logical truths. Although numerous approaches have been proposed over recent decades to address this problem, including contributions by Rantala [1982], Levesque [1984], and Fagin & Halpern [1988], the debate remains unresolved, with no definitive consensus reached. 

This situation has been recently challenged by the reintroduction of the concept of topicality by Yablo [2014]. Having a topic-sensitive logic consists in indexing by their topic; so, all logical derivations in which the consequent does not share any topic with the antecedent can now be blocked, thus blocking logical omniscience. The study of topicality is a growing field, with many scholars considering it the definitive solution to logical omniscience. But is it really so? Such an assertion warrants closer scrutiny. In order to do so, it is first necessary to restate what was being sought by modelling knowledge in modal logic and then to assess whether topicality represents a step forward or a step backward, as done, among other works, in Williamson [2024].