
Summer Meeting: Advances in Logic
17th August, 2024
Tsinghua University, Beijing, China
- Time: 10:00 AM-5:30 PM, August 17th, 2024
- Venue: Room 329. Mengminwei Humanities Building, Tsinghua University
Programme
Time |
Speaker(s) |
Title |
10:00-10:10 |
Opening |
|
10:10-10:50 |
Daisuke Ikegami (Sun Yat-Sen University) |
Preservation of AD via Forcings |
10:50-11:30 |
Lingyuan Ye (University of Cambridge) |
Intensionality via Universal Property of Arithmetic |
11:30-13:00 |
Lunch |
|
13:00-13:40 |
Liping Tang (Sun Yat-Sen University) |
A Communication Game for Linguistic Politeness in Social Networks |
13:40-14:20 |
Dazhu Li (Chinese Academy of Sciences) |
Logics of the Hide and Seek Game & Product Logics with Diagonal Constant: A Hybrid Approach |
14:20-14:30 |
Coffee Break |
|
14:30-15:10 |
Xiaoxin Jing (Capital Normal University) |
A Hybrid Modal Logic for Dynamics of Abstract Argumentation |
15:10-16:50 |
Jialiang Yan (Tsinghua University) |
Ordered Disjunction in Team-based Semantics |
16:50-17:30 |
John Lindqvist (University of Bergen) |
Distributed Belief |
18:00-20:00 |
Banquet |
Abstract

In set theory, we study models of set theory. The Axiom of Determinacy (AD) states that for any set A of binary sequences of length omega, the Gale-Stewart game with the payoff set A is determined, i.e., one of the two players has a winning strategy in the game. While AD contradicts the Axiom of Choice (AC), there are close connections between models of ZFC (Zermelo-Fraenkel set theory with the Axiom of Choice) with large cardinals and models of ZF+AD (Zermelo-Fraenkel set theory without the Axiom of Choice plus the Axiom of Determinacy).
In this talk, we discuss the relationship between models of ZF+AD and forcings (a basic tool to extend a given model M of set theory using a partial order P in M). In particular, we consider a question when partial orders preserve the truth of AD, i.e., given a model M of ZF+AD and a partial order P in M, when P produces a generic extension M[G] of M such that M[G] is a model of ZF+AD. We present several results related to this question.
This is joint work with Nam Trang from the University of North Texas.

There are many “counterexamples” of intensional meta-logical statements, like Gödel’s second incompleteness theorem. For instance, the 1960 paper of Feferman showed that if we use a different axiomatisation of PA, then PA can prove its own consistency. Or if we choose a different provability predicate, PA can also prove the corresponding consistency statements. Of course, these shouldn’t be thought of as actual evidence falsifying the second incompleteness theorem. However, it has also been extremely hard to come up with exact criteria specifying which formulation would be acceptable. In this talk, I will provide a systematic solution based on categorical logic, explaining how this perspective provides a canonical way of understanding and proving intensional meta-logical statements.

From the viewpoint of information transaction models in linguistic pragmatics, expressions of linguistic politeness (LP) induce costs upon speakers. That speakers regularly “pay” such cost is what formal models of LP typically explain either by individual-level strategic considerations (e.g., the speaker’s aim of avoiding a face-threat to the hearer) or community-level conventional considerations (e.g., the use of LP as a relation-acknowledging device). Because these explanations are compatible, as each relates to the speaker and hearer’s social relation, we combine them into a single game-theoretical model enriched by three types of social network structures (ring-shaped, star-shaped, and complete). Using simulation studies of (single and repeated) speech acts of requesting, we let the degree of LP be determined by (i) the degree of social imposition associated with a request, (ii) the number of interlocutors’ past interactions, and (iii) the relative importance of strategic and conventional considerations. The greatest average optimal degree of LP is obtained in the star-shaped network, which intuitively corresponds to a power-centered, hierarchical society.

In this talk, we extend our earlier logic for the hide and seek game with formulas from hybrid logic. Technically, this enrichment turns out to be very useful. For instance, when the previous logic tells us that the harmless-looking equality may make a logic undecidable, this extension narrows the scope of what we need to be careful about. Also, the extension is helpful in establishing complete Hilbert-style proof systems for the logic and one of its important fragments. More generally, by simply adapting our techniques, we can obtain complete proof systems for the hybrid extensions of product logics with the diagonal constant, while in literature the bare logics without the hybrid formulas are proved to be not finitely axiomatizable. Finally, we also study other topics for the logics, including the characterization of their expressive power, the advantages of our equality in defining frame properties, and the further extensions with some famous modalities proposed by Krister Segerberg in his pioneering work for product logic. This is joint work with Fenrong Liu and Katsuhiko Sano.

This paper presents a study of the dynamics of abstract argumentation frameworks from the point of view of modal logic. More specifically, we introduce a hybrid modal logic HAML, give the axiomatization of HAML, and prove the soundness and completeness of this logic. In this paper, we take abstract argumentation frameworks as Kripke frames and express arguments and attack relations by nominals and modal operators in HAML, respectively. We define acceptability criteria using valid formulas in the argumentation frame and study two kinds of modifications: adding or removing attack relations between two arguments and how the acceptance of one or more arguments can be enforced.

This talk explores the phenomenon of ordered disjunctions in natural language, where one disjunct is more emphasized than the other due to pragmatic operations. This emphasis affects the logical characteristics of disjunctions, such as the commutative law and their behavior under modal contexts. By focusing on the role of parentheses, the talk illustrates how they introduce ordered interpretations: preference, likelihood, and appropriateness of wording, differing from standard boolean readings. These interpretations are context-dependent and result in weakening the information of one disjunct. The formal account of ordered disjunctions is based on a team-based semantics, extended to capture the logical characteristics and derivation of free choice and ignorance inferences.
This talk is based on a joint work with Chen Ju and Wei Wang.

In epistemic logic, the knowledge distributed among a group of agents, or the knowledge possible given the information distributed in the group, can be formalized using the intersection modality. Distributed knowledge can potentially be resolved if the information possessed by the group is shared among its members. Formally, this is captured by turning each individual accessibility relation into the intersection of those of the group. This works because the models for knowledge are reflexive.
However, when we consider _belief_ rather than knowledge, the picture is not as simple. The cumulative information possessed by the agents can be contradictory. In such cases, the distributed belief of the group explodes: the group ends up with distributed belief in everything. Similarly, in such cases, resolving using the intersection operation makes the agents inconsistent. We consider non-explosive alternative definitions of distributed belief, both static and dynamic (resolved distributed belief). For the static case, we offer non-explosive alternative definitions for distributed belief that make use of maximal consistent subgroups. For the dynamic case, we discuss ways of preserving belief properties of individual agents.