Rui Zhu

In the paper Justification logics and hybrid logics, Melvin Fitting initiated the idea of combining justification logics and hybrid logics into a single system. However, for some technical reason, he presented a basic-hybrid justification logic JT instead of J with proving completeness theorem and realization theorem. The task of weakening this logic to J was left as an open problem in conclusion. This paper aims at solving this problem to further facilitate the proof of the properties of this logic as well as the derivation of other members of this logic family

Social Announcement Logic (SAL) is a framework for reasoning about belief diffusion in social networks, where information propagates locally based on an underlying follower structure. A key challenge in this area is to logically characterize what agents can achieve through communication, a problem often addressed using powerful but complex arbitrary announcement operators. Previous work on SAL with such operators resulted in infinitary axiomatizations, leaving the question of a finitary system open. This paper solves this open problem by presenting the first finitary, sound, and weakly complete axiomatization for a Social Announcement Logic with an arbitrary sincere announcement operator. Our central technical innovation is a novel, two-stage model transformation technique used to prove the soundness of the crucial discharge rule for arbitrary announcements. This method avoids the complex necessity-form techniques common in the literature on Arbitrary Public Announcement Logic, resulting in a more direct, Henkin-style completeness proof. Overall, the work establishes a robust and computable proof-theoretic foundation for reasoning about belief dynamics in social networks.

This paper presents a finitary axiomatization of Arbitrary Social Announcement Logic (ASAL), a dynamic epistemic logic modeling belief diffusion in social networks. ASAL extends Social Announcement Logic (SAL) with arbitrary announcement operators, resembling those in Arbitrary Public Announcement Logic (APAL). Unlike APAL, ASAL is based on belief rather than knowledge and allows inconsistent beliefs and local information flow. While ASAL shares structural similarities with Boolean APAL (BAPAL), our approach differs by avoiding the necessity form technique and instead using a novel model transformation method. We prove the soundness of the finitary axiomatization, including a derivation rule for arbitrary announcements, and establish weak completeness via Henkin-style canonical models. Illustrative examples clarify the semantic distinctions from PAL-based systems and display the model transformation process. We conclude with potential extensions of ASAL and directions for future research.