Possible worlds semantics based on observation and communication

Andreas Herzig

Emiliano Lorini

Faustine Maffre

pp. 339-362

in: Hans van Ditmarsch, Paul-Gabriel Sandu (eds), Jaakko Hintikka on knowledge and game-theoretical semantics, Berlin, Springer, 2018

Abstract

We analyze a recent trend in epistemic logic which consists in studying construction of knowledge from the agents' observational abilities. It is based on the intuition that an agent's knowledge comes from three possible sources: her observations, communication with other agents, and inference. The approaches mainly focus on the former two and suppose that the object of observations are propositional variables and that agents learn from public announcements. This allows to model knowledge in a more compact and intuitive way than with Hintikka's semantics. However, the semantics that one can find in the literature come with some counter-intuitive validities such as common knowledge of visibilities or the knowledge operator distributing over disjunctions. We propose a solution of each of these two issues and illustrate them with well-known toy examples of epistemic logic.