A computationally grounded logic of awareness
Emiliano Lorini, Pengfei Song · Journal of Logic and Computation · 2022
Abstract We introduce a multi-agent logic of explicit, implicit belief and awareness with a semantics using belief bases. The novelty of our approach is that an agent’s awareness is not a primitive but is directly computed from the agent’s belief base. We prove soundness and completeness of the logic relative to the belief base semantics. Furthermore, we provide a polynomial embedding of the logic of propositional awareness into it and a polynomial embedding of our logic into the logic of general awareness. Thanks to the latter embedding, we show that the satisfiability checking problem for our logic is PSPACE complete. Finally, we extend it by the notions of public announcement and private belief expansion.