Justifications for common knowledge

Abstract

ABSTRACT. Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of LP.We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic.

Decidability for Justification Logics Revisited

“…In order to achieve this property, we have adapted the modal techniques of filtration and generated submodels to justification logics. Apart from reproving the known decidability results for J CS , JD CS , JT CS , J4 CS , JD4 CS , and LP CS , this method has enabled us to establish the decidability of the justification logic with common knowledge introduced in [9].…”

“…A formula being satisfied at a given world is then defined as before with the following crucial case for the formula being of the form [t] B 1) E (t, B, w) holds and 2) M, v B for all v ∈ W with (w, v) ∈ R . Using a canonical model construction we can show the soundness and completeness of LP C h with respect to this class of models and as an immediate corollary of this construction (see [9,Theorem 20]) we obtain Theorem 25. LP C h (CS) is sound and complete with respect to the class of singleton models for LP C h (CS).…”

“…We can use this technique (adapted to the multi-agent case) to establish decidability for the justification logic with common knowledge LP C h that was introduced in [9].…”

“…We adapt the filtration technique from modal logic to obtain an alternative uniform proof of decidability for these justification logics. We then apply the newly developed technique to establish the decidability of the multi-agent justification logic with common knowledge presented in [9].…”

An Application of Justification Logic to Protocol Verification

“…Bucheli et al [13] introduce a justification logic with common knowledge. As an application, they study the problem of coordinated attack.…”