Arrow update synthesis

Hans van Ditmarsch (1) , Wiebe van Der Hoek (2) , Barteld Kooi (3) , Louwe Kuijer (2)

1 CELLO - Computational Epistemic Logic in LOrraine
2 Department of Computer Science [Liverpool]
3 University of Groningen [Groningen]

In this contribution we present arbitrary arrow update model logic (AAUML). This is a dynamic epistemic logic or update logic. In update logics, static/basic modalities are interpreted on a given relational model whereas dynamic/update modalities induce transformations (updates) of relational models. In AAUML the update modalities formalize the execution of arrow update models, and there is also a modality for quantification over arrow update models. Arrow update models are an alternative to the well-known action models. We provide an axiomatization of AAUML. The ax-iomatization is a rewrite system allowing to eliminate arrow update modalities from any given formula, while preserving truth. Thus, AAUML is decidable and equally expressive as the base multi-agent modal logic. Our main result is to establish arrow update synthesis: if there is an arrow update model after which ϕ, we can construct (synthesize) that model from ϕ. We also point out some pregnant differences in update expressivity between arrow update logics, action model logics, and refinement modal logic.

Mots clés: modal logic; synthesis; dynamic epistemic logic; expressivity

Domaines: Informatique [cs]

Hans van Ditmarsch, Wiebe van Der Hoek, Barteld Kooi, Louwe Kuijer. Arrow update synthesis. Information and Computation, 2020, pp.104544. ⟨10.1016/j.ic.2020.104544⟩. ⟨hal-03014108⟩