[Paper Review] Coalition and Group Announcement Logic

Rustam Galimullin, Natasha Alechina|arXiv (Cornell University)|Jul 27, 2017

Logic, Reasoning, and Knowledge4 citations

TL;DR

This paper presents Coalition and Group Announcement Logic (CoGAL), a unified framework combining Group Announcement Logic (GAL) and Coalition Announcement Logic (CAL) to reason about strategic knowledge change through public announcements. It provides a sound and complete axiomatisation using necessity forms, resolving open questions on operator interaction and establishing foundational results for epistemic logics with strategic announcement behavior.

ABSTRACT

Dynamic epistemic logics which model abilities of agents to make various announcements and influence each other's knowledge have been studied extensively in recent years. Two notable examples of such logics are Group Announcement Logic and Coalition Announcement Logic. They allow us to reason about what groups of agents can achieve through joint announcements in non-competitive and competitive environments. In this paper, we consider a combination of these logics -- Coalition and Group Announcement Logic and provide its complete axiomatisation. Moreover, we partially answer the question of how group and coalition announcement operators interact, and settle some other open problems.

Motivation & Objective

• To formalize a combined logic that integrates group and coalition announcement operators for reasoning about knowledge change in multi-agent systems.
• To address open problems on the interaction between group and coalition announcement operators in dynamic epistemic logic.
• To provide a sound and complete axiomatisation of CoGAL, extending prior work on GAL and CAL.
• To investigate the mutual expressivity and logical relationships between CAL and GAL through the new framework.
• To lay the groundwork for future extensions, including common and distributed knowledge, and decidable fragments of the logic.

Proposed method

• The paper introduces a new logic, CoGAL, by extending classical propositional logic with knowledge, public announcement, group announcement, and coalition announcement operators.
• It employs necessity forms—originally from Goldblatt’s work—to formalise infinitary rules of inference, enabling the construction of maximal consistent theories.
• A canonical model is built from maximal consistent theories to prove completeness, using a truth-preserving correspondence between formulas and their semantic interpretations.
• The proof relies on verifying that each operator's syntactic closure under inference rules matches its semantic semantics via a truth lemma.
• The completeness proof hinges on the validity of the axiom ⟨[G]⟩φ → ⟨G⟩[A\G]φ, which captures a key interaction between coalition and group announcements.
• The framework is shown to be sound and complete, with the axiomatisation being infinitary and based on necessity forms for handling complex nested modalities.

Experimental results

Research questions

• RQ1 How do group announcement and coalition announcement operators interact in a combined epistemic logic?
• RQ2 Is there a complete axiomatisation for a logic combining GAL and CAL, and if so, what form does it take?
• RQ3 What is the mutual expressivity between Coalition Announcement Logic (CAL) and Group Announcement Logic (GAL)?
• RQ4 Can the interaction between coalition and group announcements be fully characterised using logical axioms?
• RQ5 What are the limitations and extensions of the current axiomatisation, particularly regarding finitary completeness and the addition of common or distributed knowledge operators?

Key findings

• The paper provides the first sound and complete axiomatisation of Coalition and Group Announcement Logic (CoGAL), unifying GAL and CAL in a single formal system.
• The completeness proof is based on a canonical model construction using maximal consistent theories and necessity forms, ensuring that syntactic derivability matches semantic validity.
• The key axiom ⟨[G]⟩φ → ⟨G⟩[A\G]φ is shown to be valid, capturing a fundamental interaction between coalition and group announcements.
• The paper identifies that the converse of this axiom remains an open problem, leaving the mutual expressivity between CAL and GAL unresolved.
• The current axiomatisation is infinitary, and the paper leaves open the challenge of finding a finitary axiomatisation for CoGAL.
• The framework opens new research directions, including extensions with common and distributed knowledge, and the search for decidable fragments of CoGAL.