Equivalence of the information structure with unawareness to the logic of awareness

This paper proves the Li (2009) [13] unawareness structure equivalent to the single-agent propositionally generated logic of awareness of Fagin and Halpern (1988) [4]. For any model of one type one can construct a model of the other type describing the same belief and awareness. Li starts from an agent unable to perceive aspects of the world and distinguish states, modeled with subjective state spaces coarser than the objective state space. Fagin and Halpern limit the agentʼs language or cognitive ability to reasoning only about a subset of the primitive propositions describing the world. Equivalence of these approaches suggests they capture a natural notion of unawareness in a minimal way.