The Ryoan-ji Axiom for Common Knowledge on Hypergraphs

Jeffrey Kane and Pavel Naumov

The article studies common knowledge in communication networks with a fixed topological structure. It introduces a non-trivial principle, called the Ryoan-ji axiom, which captures logical properties of common knowledge of all protocols with a given network topology. A logical system, consisting of the Ryoan-ji axiom and two additional axioms, is proven to be sound and complete. [pdf]

Symmetry in Information Flow

Jeffrey Kane and Pavel Naumov

The article investigates information flow properties of symmetric multi-party protocols. It gives a sound and complete axiomatic system for properties of the functional dependence predicate that are common to all protocols with the same group of symmetries. [pdf]

Symmetries and Epistemic Reasoning

Jeffrey Kane and Pavel Naumov

The paper studies epistemic properties of symmetric communication protocols. It proposes a logical system describing properties common to all protocols with the same group of symmetries. This system is an extension of the standard epistemic logic S5 by a new axiom, capturing properties of symmetry in the modal language. The main results are soundness and completeness theorems for this logical system. [pdf]

Epistemic Logic for Communication Chains

Jeffrey Kane and Pavel Naumov

The paper considers epistemic properties of linear communication chains. It describes a sound and complete logical system that, in addition to the standard axioms of S5 in a multi-modal language, contains two non-trivial axioms that capture the linear structure of communication chains. [pdf]