November 25, 2013Mikaël Cozic (Dep. Philo UPEC, ENS Ulm)
Awareness and unawareness are a major theme in the epistemic logic literature, but it is handled there only in terms of full belief operators. The present paper aims at a treatment in terms of partial belief operators. It draws upon the modal probabilistic logic that was introduced by Aumann (1999) at the semantic level and then axiomatized by Heifetz & Mongin (2001). The paper embodies in this framework those properties of unawareness which have been highlighted in the seminal paper by Modica & Rustichini (1999). This last paper is concerned with full belief, but we argue that the properties in question also apply to partial belief in the chosen probabilistic sense. The main result is a (soundness and) completeness theorem that reunites the two strands, modal and probabilistic, of epistemic logic.