A poor man's epistemic logic based on propositional assignment and higher-order observation

Andreas Herzig (1, 2) , Emiliano Lorini (1, 2) , Faustine Maffre (1)

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 CNRS - Centre National de la Recherche Scientifique

We introduce a dynamic epistemic logic that is based on what an agent can observe, including joint observation and observation of what other agents observe. This generalizes van der Hoek, Wooldridge and colleague’s logics ECL-PC(PO) and LRC where it is common knowledge which propositional variables each agent observes. In our logic, facts of the world and their observability can both be modified by assignment programs. We show how epistemic operators can be interpreted in this framework and identify the conditions under which the principles of positive and negative introspection are valid. We also provide a sound and complete axiomatization and prove that the satisfiability problem is PSpace-complete. Finally, we show how public and private announcements can be expressed and illustrate the latter by the gossip spreading problem.

Mots clés: Dynamic epistemic logic

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

Andreas Herzig, Emiliano Lorini, Faustine Maffre. A poor man's epistemic logic based on propositional assignment and higher-order observation. 5th International Conference on Logic, Rationality and Interaction (LORI 2015), Oct 2015, Taipei, Taiwan. pp. 156-168. ⟨hal-01592020⟩