Some Notes on Temporal Justification Logic

TL;DR

This paper explores the integration of justification logic into models of knowledge and time, aiming to make the reasoning behind modalities explicit in distributed systems.

Contribution

It proposes preliminary ideas for replacing modal knowledge operators with justification logic in knowledge and time frameworks.

Findings

Conceptual framework for combining justification logic with temporal logics

Initial ideas for formalizing agent interactions with explicit justifications

Foundation for future formal development in distributed system reasoning

Abstract

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logic. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketch some preliminary ideas on how the modal knowledge part of such logics of knowledge and time could be replaced with an appropriate justification logic.