Sessions in 2022-2023 Autumn Semester
Abstract: Causal Bayesian network plays an important role in artificial intelligence, probability theory and many other fields. In some sense, we can view the scenarios we observed as a causal Bayesian network. Unlike traditional quantitative representation，in this paper, we propose a qualitative representation of causal Bayesian to explore belief revision under Bayesian network. To formalize this idea, we construct a causal plausibility model by combining the plausibility model and the causal model. We develop a logic based on this model and explore properties of the logic. (co-work with Kaibo Xie and Fenrong Liu)
Abstract: In Convention (1968), David Lewis makes the epistemic assumption that the agents have common knowledge of the convention to which they are parties, in the account of conventions, which is based on coordination problems. This became one of the most fecund but controversial developments he put forth in, that is, the study of the relation between common knowledge and social conventions. In my presentation, I will focus on how to define convention by correlated equilibrium according to Peter Vanderschraaf(1995,1998). It generalizes previous game-theoretic definitions of Lewis and can be used to characterize partial conflict situations. Examples and formal definitions will be given to show how this more extensive account of convention can be applied to some game problems as well as norms of justice.
Abstract: 对于升降原则提出的目的，当代学者各执一词。T.K. Scott(1966)认为Ockham的升降原则是量词命题的句法规则的集合，是唯名论量词理论。另一些学者，如G. Priest & S. Read(1977，1980)，则认为应该从现代真之理论的视角看，下降（上升）形式是原始句的真之条件。除此之外，P. V. Spade(1988)给出了一种更激进的看法，认为升降原则的提出是无目的性的。而本人认为，奥卡姆提出升降原则某种程度上是对于自然语言中涉及限定词单调推理的一种洞见。这一想法源自于Thomas F . Icard、Lawrence S. Moss和William Tune关于简单类型λ演算的最新成果，即通过将序关系引入简单类型λ演算来分析自然语言中的单调推理。
Abstract: This presentation is based on the paper ‘Tabularity and Post-Completeness in Tense Logic’. A new characterization of tabularity in tense logic is established, namely, a tense logic L is tabular if and only if tabTn ∈ L for some n≥1 . Two characterization theorems for the Post-completeness in tabular tense logics are given. Furthermore, a characterization of the Post-completeness in the lattice of all tense logics is established. Post numbers of some tense logics are shown.
This presentation aims to provide a formal interpretation of the why-question of action, based on a preference logic scenario. Many conceptions in natural language are incorporated, including presuppositions, sentence topics, discourse topics, etc. Compared to the other wh-questions, the why-question is unique in that it requires more satisfying answers. This analysis also provides a process for producing satisfactory answers.
Abstract: Natural Language Understanding (NLU) is a crucial problem in Artificial Intelligence (AI), and the symbolism approach to this problem lies in Formal Semantics. However, traditional theories in Formal Semantics all encounter the symbol grounding problem which prevents them successfully applying to NLU or AI. This presentation, which is based on the first part of the reporter’s doctoral dissertation, aims to give a formal solution to this problem so that one could develop a formal semantic theory more applicable to NLU and AI.
This talk is an investigation into how to define the notion of bisimulation over parity formulas. We provide and argue for a list of criteria against which we could judge how good such a definition is. In general, a notion of bisimulation should be sound, closed under union and composition, easily decidable and as close to being complete as possible. It should also guarantee the existence of a largest bisimulation, namely the bisimilarity relation. Particular to the situation with parity formulas, a good bisimulation should also have a ’relative flavor’ in its handling of the priority condition. We propose four definitions of bisimulations over parity formulas and evaluate each of them according to those criteria. We especially argue for one of the four definitions to be the best by far, since it satisfies all qualitative criteria and lies in a relatively good position onthe ’spectrum of completeness’. We also provide an adequate bisimilarity game for this notion of bisimulation which makes it easier to work with the notion.
Abstract: Argumentation has become a major research area in Artificial Intelligence over the last two decades. Abstract argumentation is an elegant way to tackle reasoning problems in the presence of conflicting information. The seminal paper by Dung defines an argumentation framework as a digraph whose nodes are abstract entities called arguments, and edges are attacks representing the conflict between these arguments. This presentation aims to introduce a dynamic epistemic logic for multi-agent abstract argumentation.
Abstract: The Laozi starts with “the dao that can be spoken of is not the constant dao”. It arises a paradox where the Laozi expresses the ineffability of the dao, but also depicts what the dao is in the text. In this presentation, we argue that the paradox of the dao is a kind of Russell’s paradox. We attempt to solve the paradox of the dao by means of solutions of Russell’s paradox and see if it would further solve the interpretive issues raised by the paradox of the dao.
What does it mean to know or believe that something might be the case? In this presentation, we address the issue focusing on the epistemic possibility expressed by English might when embedded under the propositional attitude verbs know and believe. We present some puzzles to highlight the challenges arising from such know-might and believe-might sentences. We propose a framework to solve the puzzles, in which epistemic might is defined as quantifying over the epistemic possibilities in an information state, and belief is formalized in term of a plausibility ordering. In contrast to the classical epistemic logic, the factivity of knowledge is treated as a presupposition rather than being solely dependent on the reflexivity of the accessibility relation. All analyses are implemented in a team-based modal logic BSEL, an epistemic variant of Aloni’s (2022) BSML.
This is a joint work with Maria Aloni.
In the papers ‘Losing connection: the modal logic of definable link deletion’ by Dazhu Li and ‘Relation-changing modal operators’ by Carlos Areces, Raul Fervari, and Guillaume Hoffmann, the authors put forward the definable link deletion logic, bridge logic and rotation logic, and its axiomatization are open problems. In my presentation, I will introduce some motivating examples at the beginning. Then I will illustrate the language and semantics of definable link deletion logic and bridge logic. Finally, I will give the axiomatization of definable link deletion logic and bridge logic in hybrid version, and some crucial details of completeness proof. This is a joint work with Qian Chen.
Sessions in 2021-2022 Spring Semester
Abstract: 著名汉学家瓦格纳(Rudolf G. Wagner)在《A Building Block of Chinese Argumentation: Initial Fu夫 as a Phrase Status Marker》一文指出，中国古代的分析和论证性文本中，各种修辞可以用来标记语句的身份地位，如果缺失对这方面问题的研究，我们便无法准确理解中国古代的论证。与其他语言相比，文言文中作为身份地位标记的词汇在关于论证的研究中长期被忽视。瓦格纳认为，“夫”这个词是古代哲学文本中重要的语句身份标记，他从魏晋玄学文本尤其是王弼对《周易》《老子》的注释中寻找“夫”的规范性意义。他的研究分为两个步骤，第一步是用定性和定量方法研究历史文本中业已形成的关于句首之“夫”用法的普遍意义，第二步是试图刻画出“夫”的意义、使用在历史中的发展脉络和时间线索。
Abstract: 保罗·文森特·斯佩德（Paul Vincent Spade）在‘The Logic of Categorical: The Medieval Theory of Descent and Ascent’ 一文中基于 T. K. Scott（1966）对十四世纪早期指代理论的划分，着重就第二种划分，即指代模式原则 (‘the doctrine of modes of supposition’)，给出了语义解释，语法定义，以及相应的推理规则，并就“指代模式原则”所适用的句型做了一系列规定，同时借助现代逻辑已有的结果，论证了指代模式原则中包含的三个内定理。由此进一步得出，Burley，Ockham 和 Buridan 这三位在十四世纪极具影响力的逻辑学家对于指代模式原则的语法定义本质上是一致的。
Abstract: This is a work where guarded fragment was first introduced. The aim of this work is to find natural fragments of predicate logic extending the modal one which inherit nice properties such as finite axiomatizability, Beth definability and decidability. The so-called guarded fragment enjoys nice properties.
Abstract: In the paper ‘The Logic of Public Announcements, Common Knowledge, and Private Suspicions’ by Alexandru Baltag, Lawrence S. Moss, and Slawomir Solecki, the authors put forward a new logical system that extends the epistemic logic with dynamic modalities of actions. This system is further extended with a notion of common knowledge. In my presentation, I will introduce various types of actions, such as public announcements, announcements to groups privately, announcements with suspicious outsiders, etc. I will illustrate their difference with a few examples. Finally, I will show some technical results from the paper.
Abstract: In the paper ‘A Topological Perspective on Causal Inference’ written by Duligur Ibeling and Thomas Icard, the authors put forward a general framework for topologizing spaces of causal models and characterized levels of the causal hierarchy topologically as an illustration. This work demonstrates that topologizing causal models helps clarify the scope and limits of causal inference under different assumptions. Since causal inference is the central issue for causality, I will focus on the technical results of causal inference. The proof of topological causal hierarchy theorem and some advantages of the framework will also be showed in this presentation.
In the paper ‘Formalizing Explanatory Dialogues’ written by Abdallah Arioua and Madalina Croitoru, the authors develop an argumentation framework based on Walton’s CE system on explanatory dialogue. They define the explanation in a goal-directed dialogue system governed by a set of rules. My presentation is to introduce the two main concerns in their work: the commitment stores in the dialogue and dialectical shifts. The former guarantees the success of an explanatory dialogue and the latter aims at incorporating the explanation into a wider range of different dialogues.
Ref. Arioua, M. Croitoru, Formalizing explanatory dialogues, in: International Conference on Scalable Uncertainty Management, Springer, 2015, pp. 282–297
Abstract: In the paper ‘The Problem of Logical Omniscience, written by Robert C. Stalnaker, the author first defends the deductive omniscience of an agent as a kind of idealization and explains why we need it. This work aims to clarify what the problem of logical omniscience is, which is discussed from the perspective of the sentence storage model and the question-answer machine respectively. In my presentation, I will introduce four different motivations of idealization and illustrate how the author attributes this problem to the concepts of knowledge and belief.
In this talk, I’ll introduce a new framework to provide a unifying description of different types of semantics for modal logic found in the literature and discuss their relations, using the language of topological categories. Common structures of this type include relational ones like Kripke frames, preorders, equivalence relations, etc., topological spaces, neighbourhood frames, or various other algebraic models.
From a philosophical perspective, the project can be viewed as giving a precise description of the “landscape of information”, if we identify different types of semantic models of modal logic as different ways of representing information structure. Our framework would provide a solid mathematical language to study the interplay between different information structures.
Form a technical perspective, we will provide a detailed study of the correspondence between the syntactical structure of (various extensions of) the modal language on one hand, and semantic structures of topological categories on the other hand, just like the way categorical logic does for first-order and higher-order theories. This is will allow us to obtain a conceptual understanding of the abstract structure of modal logic.
Abstract: Lyndon’s homomorphism theorem shows the equivalence between the semantic notion of monotonicity and the syntactic notion of positive occurrence. Existing proof methods either take a detour from Lyndon’s interpolation theorem, or involve complicated model constructions. In this talk, we will give a new proof method that greatly simplifies the process of model construction. In some variations of first-order logic e.g. monadic first-order logic with the infinity quantifier, a sentence upward monotonic in P is equivalent to a P-positive sentence of the same depth. Therefore, we only need to consider sentences up to a certain level of distinguishability, and have a more relaxed requirement on the models that we construct. We will show our successful attempts in monadic first-order logic with the infinity quantifier and modal logic, and analyze the difficulty we face in their combination i.e. graded modal logic.
Abstract: Carnap’s problem asks whether we can uniquely fix the semantics from a given consequence relation via a reversed Tarski-Bolzano function. Here we introduce and formulate this problem and quickly recapitulate the results in propositional and first-order logic. Then we briefly review the Hilbert system and Kripke semantics of intuitionistic propositional logic (IPC) and some intermediate logics (ICs) and formalize Carnap’s problem in IPC. Finally, we show much of IPC to be categorical, that is, fixed by the appropriate syntactic rules. However, implication remains elusive, so we show preliminary attempts at fixing it, including a limiting principle and the result in a logic above IPC, i.e., Dummett logic (LC).
Abstract: Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. In this talk, we study temporal dependence in dynamical systems from a logical perspective, by extending a minimal modal base logic of static functional dependencies. We define a logic for dynamical systems with single time steps, provide a complete axiomatic proof calculus, and show the decidability of the satisfiability problem for a substantial fragment. The system comes in two guises: modal and first-order, that naturally complement each other. Next, we consider a timed semantics for our logic, as an intermediate between state spaces and temporal universes for the unfoldings of a dynamical system. We prove completeness and decidability by combining techniques from dynamic-epistemic logic and modal logic of functional dependencies with complex terms for objects. Also, we extend these results to the timed logic with functional symbols and term identity. Finally, we conclude with a brief outlook on how the system proposed here connects with richer temporal logics of system behavior, and with dynamic topological logic. The talk is based on recent joint work with Alexandru Baltag and Johan van Benthem.
Sessions in 2021-2022 Autumn Semester
Abstract: Neighborhood semantics for modal logic is generalized in a two-sorted way in instantial neighborhood logic(INL). As a following-up work of INL, we develop another semantics for the INL language and then get exclusively instantial neighborhood logic(EINL). It is able to talk about distinct existential information in a single neighborhood, and has an expressive power strictly stronger than that of INL. We offer a Hilbert-style axiomatization of EINL, whose weak-completeness is shown by the technique of extended normal form. Finite model property and decidability for EINL are obtained as well. This is a joint work with Dazhu Li and Junhua Yu.
Abstract: The two dominant approaches to the psychology of causal induction—the covariation approach and the causal power approach—are each crippled by fundamental problems. This talk will introduce P.W. Cheng’s article which proposes an integration of these approaches that overcomes these problems. The proposal is that reasoners innately treat the relation between covariation and causal power as that between scientists’ law or model and their theory explaining the model. This solution is formalized in the power PC theory, a causal power theory of the probabilistic contrast model.
Abstract: A finitely alternative normal tense logic Tn,m is a normal tense logic characterized by frames in which every point has at most n future alternatives and m past alternatives. The structure of the lattice Λ(T1,1) is described. There are ℵ0 logics in Λ(T1,1) without the finite model property (FMP), and only one pretabular logic in Λ(T1,1). There are 2ℵ0 logics in Λ(T1,1) which are not finitely axiomatizable. For nm≥ 2, there are 2ℵ0 logics in Λ(Tn,m) without the FMP, and infinitely many pretabular extensions of Tn,m.
Abstract: Various kinds of interrogative sentences play an essential role in natural language and the study of them is an intersection area of linguistics, logic and philosophy. However, there are relatively less works with respect to why-interrogatives. In this proposal, I will give an informal sketch of the difficulties of the study of why-interrogatives from semantic and pragmatic perspectives. And then I will introduce several semantic formulations and logics of interrogation to see if it is possible to give an explanation of why-interrogatives in a formal way.
Abstract: The idea of distributed games comes from distributed systems, which are often used in computer science to describe the combination of parallel processes. There are several mechanisms to provide operational models for distributed systems by means of transition systems. We provide a logical characterization of distributed systems reflecting the handshaking mechanism. Furthermore, we try to explore knowledge and strategies from the perspective of games.
Abstract: 威廉•舍伍德的《逻辑学导论》（Introductiones in logicam）是中世纪晚期新式逻辑（logica moderna）时期最早的完整著作，该书中关于词项特性的分析与其另一本著作《助范畴词》（syncategoremata）关于助范畴词的论述奠定了新式逻辑发展初期的两个主要研究路径：词项特性和助范畴词，而对后者的研究又是以前者为理论基础。舍伍德将词项特性分为：意谓特性（signification），指代特性（supposition），连接特性（copulation）和称呼特性（appellation），其中指代特性是舍伍德最为关注的部分，而由此建构起来的指代理论可以说是舍伍德词项特性理论的核心。即便是更广为人知的威廉•奥卡姆的指代理论，其理论基础也要追述到舍伍德的思想。因此，无论是从窥探威廉•舍伍德整个理论架构，还是从中世纪晚期逻辑学思想史的角度，厘清威廉•舍伍德的指代理论都是首要之选。
Abstract: The curve fitting problem is on finding the curve that best fits a number of data points. The philosophical interest mainly lies in justifying trade-off of simplicity and goodness-of-fit. Several solutions have been proposed based on different concepts, like Akaike’s Information criterion, Bayesian information criterion, and Bayes’s theorem criterion etc. In this talk I will present some basic solutions and compare them.
Sessions in 2020-2021 Spring Semester
- Peng Cui 崔鹏
- Ke Deng 邓柯
- Yang Sun 孙洋: Deontic logic as founded on nonmonotonic logic
- Yuqi Liu 刘雨琦: Epistemology without Knowledge and Belief
- Lingyuan Ye 叶凌远: Uniformity, Contingency, and Self-reference in arithmetic
- Lei Li 李磊: On link deletion and point deletion in games on graphs
- Xiao Li: Towards a semantic concept of aboutness: a proposal
- Mingliang Chu: 中世纪逻辑学
- Kaibo Xie 谢凯博: 关于研究方向选择的一些想法
- Gengjun Yao 姚庚君: 当传播学遭遇数理逻辑
- Huanfang Dong 董焕防: Basics of Recommendation Systems
- Chi Gao 高驰: 时序知识图谱的可解释预测