Second-order propositional announcement logic

Francesco Belardinelli (1) , Hans van Ditmarsch (2) , Wiebe van Der Hoek (3)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 CELLO - Computational Epistemic Logic in LOrraine
3 University of Liverpool

In this paper we introduce Second-order Propositional Announcement Logic (SOPAL): a language to express arbitrary announcements in Public Announcement Logic, by means of propositional quantification. We present SOPAL within a multi-agent context, and show that it is rich enough to express complex notions such as preservation under arbitrary announcements, knowability, and successfulness. We analyse the model theory of SOPAL and prove that it is strictly more expressive than Arbitrary PAL [2], and as expressive as Second-order Propositional Epistemic Logic [4], even though exponentially more succinct than the latter. These results points to a rich logic, with nice computational properties nonetheless, such as a decidable model checking problem and a complete axiomatisation.

Mots clés: Autonomous agents; Computation theory; Model checking; Multi agent systems Axiomati-sation; Computational properties; Epistemic logic; Model checking problem; Model theory; Multi agent

Domaines: Système multi-agents [cs.MA]

Francesco Belardinelli, Hans van Ditmarsch, Wiebe van Der Hoek. Second-order propositional announcement logic. 15th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2016), May 2016, Singapore, Singapore. pp.635--643. ⟨hal-01492518⟩