The Logic of Data Access and Data Exchanges

2026-06-30

AI Summary

This study addresses the formal characterization of agents’ non-propositional knowledge concerning variable values in data access and exchange, along with its dynamic evolution. To this end, the work proposes an extended dynamic epistemic logic that integrates propositional knowledge with conditional non-propositional knowledge. The framework introduces a generalized knowledge operator capable of restricting the range of possible values and employs definite descriptions based on a minimization operator to enable naming and comparison of hypothetical values. It provides a unified semantics for modeling diverse data-exchange events—such as private announcements, database theft, and open-source sharing—and establishes a fully axiomatized system. The paper further proves the decidability and bisimulation invariance (co-expressivity) of the resulting logic.

Abstract

We investigate a new logic that extends Dynamic Epistemic Logic (DEL), by combining standard epistemic modalities for (individual and distributed) propositional knowledge with operators for (conditional) non-propositional knowledge of a number (in which an agent or a group have knowledge of the value of some variable x, conditional on some additional information). We also generalize these operators, by considering formulas that express the fact that an agent or group can (conditionally) narrow down the possible values of the variable x to at most N possibilities (for some natural number N). In order to name and compare such hypothetical values, we extend the logic further with definite descriptions based on minimization operators, denoting the least of the N possible values of x (according to some fixed order) that are considered possible by the agent or group. On this static base, we consider DEL-style extensions with dynamic modalities for general 'data-exchange events' (covering private and public propositional announcements, but also secret hacking of a private database, or public sharing of one's data via open-source repositories, etc.). In such scenarios, whole 'chunks' of information may be exchanged or modified: once access to a given source is gained, all the 'data' stored at that specific location becomes available. We give complete axiomatizations for the resulting logics, and prove their decidability and co-expressivity.

Problem

• Dynamic Epistemic Logic
• non-propositional knowledge
• data exchange
• conditional knowledge
• epistemic logic

Innovation

• Dynamic Epistemic Logic
• non-propositional knowledge
• data-exchange events
• definite descriptions
• decidability