Arrow Update Synthesis

TL;DR

This paper introduces AAUML, a dynamic epistemic logic with arrow update models, providing axiomatization, decidability, and a synthesis method for constructing updates that achieve specific formulas.

Contribution

It presents the first axiomatization and synthesis method for arrow update models, expanding the expressivity and applicability of dynamic epistemic logics.

Findings

AAUML is decidable and as expressive as multi-agent modal logic.

A rewrite system allows elimination of arrow update modalities while preserving truth.

Synthesis of arrow update models from formulas is possible.

Abstract

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 axiomatization 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 phi, we can construct (synthesize) that model from phi. We also point out some pregnant differences in update expressivity between arrow update logics, action model logics, and refinement modal logic.