A composable language for action models

TL;DR

This paper introduces a new syntactic language for representing action models in epistemic logic, enabling intuitive descriptions and effective synthesis up to certain modal depths with sound and complete axiomatizations.

Contribution

It proposes a composable, syntactic language for action models that simplifies their representation and analysis compared to traditional semantic structures.

Findings

The language can represent any action model up to a certain modal depth.

It effectively captures the results of action model synthesis.

Provides sound and complete axiomatizations in specific settings.

Abstract

Action models are semantic structures similar to Kripke models that represent a change in knowledge in an epistemic setting. Whereas the language of action model logic embeds the semantic structure of an action model directly within the language, this paper introduces a language that represents action models using syntactic operators inspired by relational actions. This language admits an intuitive description of the action models it represents, and we show in several settings that it is sufficient to represent any action model up to a given modal depth and to represent the results of action model synthesis, and give a sound and complete axiomatisation in some of these settings.