Action models for knowledge and awareness

We consider semantic structures and logics that differentiate between being uncertain about a proposition, being unaware of a proposition, becoming aware of a proposition and getting to know the truth value of a proposition. In this paper we give a unified setting tomodel all this variety of static and dynamic aspects of awareness and knowledge, without any constraints on the modal properties of knowledge (or belief — such as introspection) or on the interaction between awareness and knowledge (such as awareness introspection). Our primitive epistemic operator is called speculative knowledge. This is different from the better known implicit knowledge, now definable, which plays a more restricted role. Some dynamic semantic primitives that are elegantly definable in our setting are the actions of ‘becoming aware of a propositional variable’, ‘implicit knowledge’, ‘addressing a novel issue in an announcement’, and also more complex ways in which an agent can become aware of a novel issue byway of increasing the complexity of the epistemic model.