Group Knowledge of Hypothetical Values

2025-11-27

AI Summary

Existing dynamic epistemic logics inadequately model semi-public data exchanges—such as public announcements, group-restricted sharing, and variable assignments—limiting their applicability to realistic information-sharing scenarios. Method: We propose an extension of epistemic logic with variable-aware knowledge operators. Our approach introduces modal operators for semi-public events, defines conditional distributed knowledge and hypothetical value descriptors, and—novelty—introduces *conditional common distributed knowledge* to precisely capture group-level coordinated knowledge about variable values under assumptions. Contribution/Results: We construct the first sound and complete axiomatization covering semi-public interactions, prove its decidability, and support formal verification via equational reasoning and propositional conditioning. Case studies demonstrate the framework’s effectiveness in modeling incremental, context-sensitive information sharing—e.g., multi-agent coordination with partial observability and conditional commitments.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In recent years, epistemic logics have been extended with operators K_ax for knowledge of (the value of) a variable x (by an agent a). We study dynamic versions of these logics, enriched with modalities for semi-public data-exchange events (e.g., public announcements, data-sharing within a subgroup, or changing the value of a variable). To obtain a complete axiomatization of data-exchange events, in the presence of equality x = y and K_ax, one needs to extend the logic further: first, with an operator for distributed knowledge K_Ax of the value (by a group of agents A); next, with a conditional version of this: distributed knowledge K^P_A x (of the value by a group) given some hypothetical condition (expressed by some proposition P); then, with definite descriptions x^P_A , denoting the 'hypothetical' value of x according to A's (distributed) knowledge given condition P. In order to deal with common knowledge in the presence of semi-public data exchanges, we also need to add a novel conditional version of the recent concept of common distributed knowledge. We investigate the resulting logic, giving examples and presenting a complete axiomatization and a decidability proof.

Problem

• Extends epistemic logic with operators for group knowledge of variable values
• Introduces dynamic modalities for semi-public data-exchange events
• Develops conditional distributed knowledge and hypothetical value descriptions

Innovation

• Extends epistemic logic with distributed knowledge operators
• Introduces conditional distributed knowledge for hypothetical scenarios
• Adds novel conditional common distributed knowledge for data exchanges