Social Announcement Logic

Abstract

Social Announcement Logic (SAL) is a formal framework for modeling information dynamics in social networks, augmenting epistemic logic with operators for communication. A significant open challenge in this field is developing sound and complete finitary axiomatizations for logics that include arbitrary announcements, a problem underscored by known soundness issues in Arbitrary Public Announcement Logic (APAL). This thesis addresses this challenge by first establishing a novel semantic framework for SAL based on sets of propositions rather than standard Kripke models. The central contribution is the development of a new model transformation technique to prove the soundness of the inference rule for arbitrary announcement operators. This constructive, model-based method provides a transparent semantic justification for this crucial inference rule. This technique enables the primary result of the thesis: the first sound and complete finitary axiomatization for Arbitrary Social Announcement Logic (ASAL). The research further supports this system by developing a complementary tableau system for efficient theorem proving and model construction. Additionally, the thesis analyzes the expressive power of SAL, demonstrating how various classes of coherence models make it possible to define the social network’s following relationship using purely epistemic formulas. By establishing these formal systems and novel proof methods, this thesis provides a robust framework for analyzing belief dynamics in social networks. It offers a new, verifiable solution to persistent challenges in the logic of arbitrary communication, with implications for epistemology, computer science, and the analysis of multi-agent systems