Tsing Ch’a Past Session from 2025

The integration of temporal reasoning with agency—the formalization of how agents make choices over time—is a foundational area of study in philosophy and logic. Temporal logic and STIT (Seeing to It That) logic have been well-established separately, with complete axiomatizations existing for both systems. Temporal STIT (TSTIT) logic combines temporal operators with STIT operators to model agency over time. While there has been some prior work on the axiomatization of TSTIT logic, existing results are limited to specific classes of STIT frames, leaving the general axiomatization problem open. In this talk, we will focus on the axiomatization of TSTIT logic with temporal operators X, F, and the STIT operator for a single agent, interpreted over discrete time and bundled trees. Specifically, we will explore a transformation method involving bundled trees and Ockhamist frames, which aims at constructing a general STIT frame.

This is a joint work with Zhang Yan.

Disjunctive dependence is an interesting variant of functional dependency, which is used to express dependency like “x functionally determines y or z”. In this talk, I will discuss representation theorem for disjunctive dependence in dependence models and present some negative and positive results on it.

When faced with complex epistemic-combinatorial situations, agents struggle to formally differentiate between relational patterns, creating gaps in formal models.

To address this, we introduce strictly relevant operators and construct an Epistemic Logic based on Possible Knowledge Bases (EL_{PKB}). Among these, these new operators require not only the absence of counterexample situations but also every truth cases must exist, ensuring a precise representation.

To this end, we introduce a non-Kripke model that incorporates PKBs to define the semantics. In this context, a PKB refers to the knowledge combinations that an agent might possess in a given state. Then we explore the correspondence between PKBs under different definitions and the cognitive properties of agents.

In the end, we try to provide sequent calculus for this logic.

This is a report of this paper: Jalali, Raheleh. “Proof complexity of substructural logics.” Annals of Pure and Applied Logic 172.7 (2021): 102972.

Donald Sturgeon’s Ph.D thesis is an inquiry of the epistemology in early China. In this thesis, he argues that in early Chinese thought, some key concepts from the Western tradition of philosophy—such as truth and belief—did not play a particularly important role in understanding knowledge. Meanwhile, action and the capacity for correct action constitute the core elements of the Chinese conception of knowledge, forming a stark contrast with the JTB-like account of knowledge that excludes the factor of action.

In this talk, I will introduce the three main chapters of his thesis. The thesis first discusses the problem of knowledge acquisition. In early China, people agreed that knowledge derives on one hand from the heart-mind (心) and sensory organs, and on the other hand from practical training or cultivation leading. However, philosophers had fundamental disagreements about what ultimately determines what counts as knowledge. Secondly, knowledge was generally conceived as systematically correct action, and thus linguistic knowledge is the correct use of language. Language plays a crucial role in expressing and transmitting knowledge, and can therefore guide action to make it conform to the correct dao. This key function depends on objective standards for language use, but the standards was challenged by skepticism. The thesis finally discusses Zhuangzi’s skepticism and argues that his skepticism to some extent improved our epistemic position.

References

1. Donald Sturgeon, 2014. Knowledge in Early Chinese Thought. Ph.D Thesis, University of Hong Kong.

This talk presents a theoretical and computational study of belief dynamics in social networks using a threshold automaton model. We disprove the universal stability conjecture of belief convergence proposed by Liu et al. (2014), demonstrating instead that original formulation of the conjecture is exclusively achieved in finite, strongly connected networks. Our analysis establishes complete convergence conditions, generalizes stability criteria that extend beyond the original conjecture, and reveals that oscillating networks are equivalent to bipartite networks. The results provides a strict upper bound of time required for network stability, and by combining the six degrees of separation theory, it can be concluded that under this model, all humanity will stabilize in an extremely short time. These findings are further corroborated through experimental validation via simulation studies.

References

1. Liu, F., Seligman, J. & Girard, P. Logical dynamics of belief change in the community. Synthese 191, 2403–2431 (2014). https://doi.org/10.1007/s11229-014-0432-3

Arbitrary announcement operators are dynamic modalities that quantify over all possible messages that can be announced. They enable the expression of whether a given formula remains valid under any such announcement, thereby significantly enhancing the expressive power of Social Announcement Logic (SAL) in modeling information flow. However, incorporating such operators presents major formal challenges, particularly in proving the soundness of inference rules and establishing finitary completeness. In this work, we introduce a model transformation technique that provides a soundness proof for key inference rules involving arbitrary announcements. Based on this result, we construct a finitary axiomatization of SAL and prove its weak completeness using a standard Henkin-style method. We conclude by discussing the potential application of this technique to more complex scenarios, including reasoning about higher-order beliefs and dynamic changes in network structure. This talk is based on a paper accepted for presentation at LORI 2025.