A Probabilistic Temporal Epistemic Logic

TL;DR

This paper introduces PTEL, a probabilistic temporal epistemic logic that models uncertain knowledge of agents over time, with formal semantics, axiomatization, and completeness proof.

Contribution

It presents a new expressive logic combining probability, time, and knowledge, with formal semantics and a proof of strong completeness.

Findings

Defined semantics for PTEL using Kripke models with probabilistic and temporal components

Provided an axiomatization and proved strong completeness of PTEL

Established a formal framework for reasoning about uncertain knowledge over time

Abstract

We introduce an expressive probabilistic temporal epistemic logic PTEL suitable to reason about uncertain knowledge of a non-rigid set of agents that can be changed during time. We define semantics for PTEL as Kripke models with epistemic accessibility relations for agents' knowledge, linear temporal relations describing possible runs of the system, and probability functions defined on sets of runs. We give an axiomatization of PTEL and sketch the proof of strong completeness.