A Logic of Belief and Omission

Here we present a modal logic that emerged when considering the interactions of awareness and knowledge. Whereas knowledge is described by those propositions that are true in every world the agent considers possible, awareness is described by the propositions that the agent perceives as either true or false, in any world. As such, we can model an agent who ignores the existence of a proposition in the context of some possible worlds. The resulting logic is able to capture reasoning free of logical omniscience, where an agent may, consciously or unconsciously omit facts and deductive rules from their arguments.