Dynamic Logic of Trust-Based Beliefs

TL;DR

This paper develops a dynamic logic framework for modeling beliefs based on data, incorporating public data announcements, with a complete axiomatisation and an efficient model checking algorithm.

Contribution

It introduces a novel logical system that captures the interaction between data-driven beliefs and data announcements, with formal soundness, completeness, and polynomial model checking.

Findings

Sound and complete axiomatisation of the logic.

Polynomial model checking algorithm.

Formal analysis of data-informed belief dynamics.

Abstract

Traditionally, an agent's beliefs would come from what the agent can see, hear, or sense. In the modern world, beliefs are often based on the data available to the agents. In this work, we investigate a dynamic logic of such beliefs that incorporates public announcements of data. The main technical contribution is a sound and complete axiomatisation of the interplay between data-informed beliefs and data announcement modalities. We also describe a non-trivial polynomial model checking algorithm for this logical system.