JRC for Logic
Tsinghua University – University of Amsterdam Joint Research Centre for Logic
JRC for Logic
Tsinghua University – University of Amsterdam Joint Research Centre for Logic

Past Sessions

Sessions in 2024-2025 Fall Semester

Abstract:

Computational Cognitive Science is an interdisciplinary field seeking to understand human cognition and intelligence through computational principles. Logic has played fundamental roles in the early development of cognitive science, and keeps influencing today’s most cutting-edge research in the field. In this talk, I will briefly introduce the historical connection between logic and cognitive science, and share some of my work combining formal representations, probabilistic inference, and behavioral experiments, to account for how people synthesize concepts from very few data and generalize to novel situations.

Abstract:

I will talk about the interface of the determinacy of Gale-Stewart games and automata on infinite words. The Gale-Stewart game is a two-player turn-based game with perfect information. Given a winning set X, determinacy of X asserts that one of the two players has a winning strategy. The winning set X can also be defined by variants of finite automata as a set of infinite words accepted by such automata. I will review several variants of finite automata on infinite words and the determinacy studies along this topic, then introduce our studies on determinacy strength of infinite games with winning sets defined by pushdown and probabilistic automata with various acceptance conditions.

Abstract:

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. However, when we consider belief rather than knowledge, the picture is more complicated. 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. 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.

Abstract:

Poison modal logic and poison sabotage modal logic have been studied in the existing literature to capture the so-called poison game, which was originally conceived as a paradigm for reasoning about graphical concepts in graph theory and has recently been shown to have significant applications in the theory of abstract argumentation. In this work, we further explore the technical aspects of these two logics and extend existing results by addressing the open questions identified in [Grossi and Rey, 2019, Blando et al., 2020]. Specifically, we show that poison sabotage modal logic has an undecidable satisfiability problem, and we provide both Hilbert-style calculus and tableau calculus for these logics. This is a joint work with Fenrong Liu and Dazhu Li.

Abstract:

In paraconsistent logic, the Principle of Explosion (ECQ) does not hold, meaning that both a proposition A and its negation ¬A can be true at the same time. In this talk, I will briefly introduce Non-adjunctive Discursive Logic and Paraconsistent Logic with Preservationism, which introduce the concept of sets of inconsistent formulas. I will then build a model composed of inconsistent sets, where these inconsistent formulas can be derived. I will also discuss the relationship between this model and the Kripke model. Furthermore, I will provide a characterization of the semantics for some classes of frames and explore more results on compactness. This talk is based on my master’s thesis.

Abstract:

In Baltag and van Benthem’s paper [1], three representation theorems are proved for the functional dependence relation (Proposition 2.6). In this talk, we will simplify the construction which is key to the proof. Based on this simplification, we give a more detailed characterization of the construction. We will also disscuss other representation theorems in other related works.

References
[1] Baltag, A., van Benthem, J. A Simple Logic of Functional Dependence. J Philos Logic50, 939–1005 (2021). 

Abstract:

Baltag and van Benthem[1] introduced a logic of functional dependence (LFD) with local dependence formulas and dependence quantifiers, which can be seen both as a first-order and a modal logic. In the relational semantics of LFD, the dependence quantifiers become modalities and local dependence formulas are treated as special atoms. In particular, the modalities involving multiple variables correspond to intersections of relations. This leads to the study on the interaction between LFD and Boolean Modal Logic [2] (BML)—a poly-modal logic where families of binary relations are closed under the Boolean operations of union, intersection, and complement.In this talk, I will present a BML version of LFD, which can express additional notions of dependence. I will provide an axiomatization, including details about its completeness proof. Furthermore, I will extend the framework by introducing conditional independence atoms, and propose an axiomatization for the extended logic.

This is joint work with Chenwei Shi and Qian Chen.

Reference：

[1] Baltag, Alexandru, and Johan van Benthem. “A simple logic of functional dependence.” Journal of Philosophical Logic 50 (2021): 939-1005.

[2] Gargov, George, and Solomon Passy. “A note on Boolean modal logic.” Mathematical logic. Boston, MA: Springer US, 1990. 299-309.

Abstract:

Multi-Structural (MS) games and their variants are designed to capture the number of quantifiers needed to express first-order properties. Recently, Carmosino et al. [1] employed MS games to establish tight bounds on the the number of quantifiers needed to define specific properties of ordered structures. In this talk, I will use the techniques and findings from [1] to show that, on the class of finite linear orders, any first-order sentence with a quantifier depth of n is equivalent to a sentence with approximately 2n quantifiers. Furthermore, I will discuss some potential applications of these games in investigating the succinctness of the finite-variable fragments of first-order logic on linear orders.

Reference:

1. Carmosino, M., Fagin, R., Immerman, N., Kolaitis, P., Lenchner, J., & Sengupta, R. (2024). On the number of quantifiers needed to define boolean functions. arXiv preprint arXiv:2407.00688.

Abstract:

Sets paired with a distinguished collection of subsets, known as subset spaces, are ubiquitous in many areas. In 1996, Andrew Dabrowski, Lawrence S. Moss and Rohit Parikh presented a bimodal logic suitable for formalizing reasoning about points and sets, and also states of the world and views about them. The truth of a formula is defined in a point-set pair. Since the logic involves two modalities, this naturally corresponds to Kripke models with two interrelated relations, termed a cross model. It is known that a cross model can be derived from a subset space model, but the problem of the reverse transformation remains unsolved. In this talk, we explore a possible transformation from a cross model back to a subset space model.


Reference：

  1. Dabrowski A, Moss L S, Parikh R. Topological reasoning and the logic of knowledge[J]. Annals of Pure and Applied Logic, 1996, 78(1-3): 73-110.

Abstract:

Intuitionistic Probability Logic ILP, which intended to provide an Intuitionistic formalization of reasoning about probability, was proposed by Angelina Ilić-Stepić et al. An objective of this presentation is to introduce a translation from ILP formulas to a new language which is designed to split the occurrence of probability intervals in ILP formulas into a minimum consideration range. Also, I will give a tableau based on the new language.

Abstract:

Coalition Logic (CL) is a standard and successful logic for reasoning about coalitional power, captured by both effectivity functions from cooperative game theory and (strategic) game forms from non-cooperative game theory, thanks to the representation theorem of truly playable effectivity functions by game forms (see [1]).The axiom of superadditivity in CL precludes dependence between different coalitions’ actions, which is nevertheless ubiquitous. It is natural to ask how to develop a generalization of CL that allows dependence, and can be used to reason about effectivity functions and game forms that allow dependence, which we formulate as dependence-friendlily playable effectivity functions and game forms allowing dependence respectively.In this talk, we will first show our representation theorem of dependence-friendlily playable effectivity functions by game forms allowing dependence. We will then define Coalition Logic Allowing Dependence (CLD), for which we provide a neighbourhood semantics based on effectivity functions and a Kripke semantics based on game forms allowing dependence. We will demonstrate the finite model property of CLD with respect to its neighbourhood models, and in virtue of our representation theorem, prove that CLD is sound and weakly complete with respect to its neighbourhood and Kripke frames.This is joint work with Chenwei Shi.

Reference：

  1. Valentin Goranko, Wojciech Jamroga, and Paolo Turrini. Strategic games and truly playable effectivity functions. Autonomous Agents and Multi-Agent Systems, 26:288–314, 2013.

Abstract:

‘The principle of alternative possibilities’ (PAP), stating that ‘a person is morally responsible for what he has done only if he could have done otherwise,’ has long been central to discussions of moral responsibility. However, Frankfurt’s [1] counterexamples, which challenge PAP, have shifted scholarly focus to actual-sequence views.In this talk, I will introduce an interpretative approach that incorporates an epistemic dimension of alternative possibilities, arguing that while we intuitively consider alternative possibilities when ascribing responsibility, this consideration operates at an epistemic rather than a purely factual level.

Utilizing Canavotto’s [2] refinement of STIT, I will first outline the factual perspective of alternative possibilities and examine the ‘orthodox’ theory proposed by Fischer and Ravizza [3] along with its possible objections. Then, by extending the model with an epistemic (or doxastic) relation, we emphasize the epistemic aspect of alternative possibilities.

References:

[1] Frankfurt, H. (1969). Alternate Possibilities and Moral Responsibilities. Journal of Philosophy, 66, pp. 829-839.
[2] Canavotto, I. (2022). Where Responsibility Takes You: Logics of Agency, Counterfactuals, and Norms. Cham: Springer.
[3] Fischer, J. M., & Ravizza, M. (1998). Responsibility and Control: A Theory of Moral Responsibility. New York: Cambridge University Press.

Sessions in 2023-2024 Spring Semester

Abstract:

Link variations, including link cutting, adding and rotating, are critical updating process on graphs, which play important roles in graph reasoning. Undefinable link variations and their logics have been widely studied. In [Li, 2020], Li introduced a modal logic, LLD, designed for definable link cutting. In this talk, following LLD, I will propose the logics LLA, LLR, and LLV, which respectively address definable link adding, rotating, and combinations of dynamic operations on graphs. Van Benthem-style characterization theorems for these logics will be provided. In addition, I will show that all these logics are undecidable and present decidable fragments of them.
This is a joint work with Qian Chen.

Abstract:

This talk will give an introduction to Woodin’s generic absoluteness theorem for the Chang model. In particular, we will show that if there exists a Woodin cardinal which is a limit of Woodin cardinals, then every set of reals in the Chang model is Lebesgue measurable. The proof presented here follows the approach developed in Paul Larson’s book The Stationary Tower.This is joint work with Jialiang Yan.

Abstract:

The differing views on individual terms prompt us to consider Ockham’s rules of ascent and descent from various perspectives. Firstly, interpreting individual terms as elements within the domain of individuals, we see the ascent and descent rules as part of the quantification theory in first-order logic. Secondly, adopting Quine’s approach, which views individual terms as a specific kind of predicate, we interpret the rules within the tradition of the Two-Classes Theory. We believe this interpretation aligns more closely with Ockham’s original intent. Moreover, from this viewpoint, the ascent and descent rules closely coincide with the pattern of monotonic reasoning that represents ‘predicate substitution‘. Finally, to ensure the surface syntactic structure remains unchanged, we draw upon Russell’s theory of descriptions, interpreting individual terms as collections of properties. We will demonstrate that, within the framework of generalized quantifiers, the ascent and descent rules constitute a form of monotonic reasoning.

Abstract:

The formal study of argumentation plays an important role in knowledge representation, especially in reasoning from contradictory information. Many developments build on Dung’s seminal theory of argumentation. Preference is a key concept in argumentation to represent the comparative strength of arguments, and in particular can be used to resolve conflicts between arguments. It’s essential for preferences to adapt to various scenarios rather than remaining fixed. Consequently, Modgil extended Dung’s framework to reasoning about preferences. However, this extension led to the loss of the general existences of grounded and preferred extensions. In this talk, I will begin with an introduction to Dung’s abstract argumentation framework and semantics, followed by an introduction to Modgil’s extended argumentation framework and semantics. Then I will explain the limitations of Modgil’s semantics. At last, I will present our new semantics based on the extended argumentation framework, which preserves the semantic properties of Dung’s argumentation framework.

This is a joint work with Yan Zhang. 

Abstract:

In the digital era, users encounter an endless stream of recommendations. The development of recommendation algorithms in AI has attracted extensive attention, yielding a substantial body of literature. However, the contribution of logic has been minimal. In this talk, we propose a new recommendation logic (RL) to study the reasoning behind recommendations, emphasizing their basis in users’ revealed preferences. We explore the expressivity of RL by introducing a new notion of bisimulation and translating RL into a 3-variable fragment of a two-sorted first-order logic. We show that RL-models have the tree model property and that their model-checking problem can be solved in polynomial time, for which we propose an algorithm and prove its correctness. We believe that our approach lays a foundation for AI research and has the potential to advance personalized recommendations.

This is joint work with Fenrong Liu and Sisi Yang.

Abstract:

Games can serve as a tool to characterize the expressive power of logics. One example is the Ehrenfeucht-Fraïssé Games (EF-games), which capture the quantifier rank of first-order sentence required to distinguish between two structures. In my presentation, I will discuss combinatorial games that have garnered attention recently, particularly focusing on multi-structural games introduced in [1] and re-discovered in [2]. These games can capture the number of quantifiers of first-order sentences required to separate structures. I will present the findings from [3] regarding the differences between EF games and the multi-structural games. Moreover, I will discuss syntactic games introduced in [3], which can simultaneously capture reasonable syntactic measures and the number of variables of first order sentences.

This talk is mainly based on [3].

References

[1] Immerman, N. (1981). Number of quantifiers is better than number of tape cells. Journal of Computer and System Sciences, 22(3), 384-406.

[2] Fagin, R., Lenchner, J., Regan, K. W., & Vyas, N. (2021, June). Multi-structural games and number of quantifiers. In 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (pp. 1-13). IEEE.

[3] Carmosino, M., Fagin, R., Immerman, N., Kolaitis, P., Lenchner, J., & Sengupta, R. (2023). Multi-Structural Games and Beyond. arXiv preprint arXiv:2301.13329.

This is joint work with Fenrong Liu and Sisi Yang.

Abstract:

This presentation aims to derive general heuristics and specific methods for axiomatization, the Finite Model Property (FMP) and decidability. It will encompass selected excerpts from my recent papers [Knudstorp 2023b; Knudstorp 2023a], along with unpublished work, extending my Master’s thesis (https://eprints.illc.uva.nl/id/eprint/2226/1/MoL-2022-24.text.pdf), ‘Modal Information Logics’, overseen by Johan van Benthem and Nick Bezhanishvili.

Modal information logics (MILs) were first proposed by Van Benthem (1996) to model a theory of information using possible-worlds semantics. Although the logics have been around for some time, not much is known: Van Benthem (2017) and Van Benthem (2019) pose two problems, namely (1) axiomatizing the two basic MILs of suprema on preorders and posets, respectively, and (2) proving (un)decidability.

The main results of the first part of the talk are solving these two problems: (1) by providing an axiomatization [with a completeness proof entailing the two logics to be the same], and (2) by proving decidability ‘via completeness’.

The second part of the talk will explore a selection of belated logical systems. Most notably, the MIL on semilattices is axiomatized with an infinite scheme and shown not to be finitely axiomatizable. Emphasis will be limited to two main aspects: the axiomatization technique employed, and the (seemingly) paradoxical increase in complexity: from the finitely axiomatizable (decidable) MILs on preorders and posets, an infinitely (and not finitely) axiomatizable (undecidable) logic arises by chaffing away most of the posets to only consider the more well-behaved ones with all binary suprema.

The talk will be entirely self-contained, yet attendees may find my Peking talk on April 9th to be a valuable supplement.

References

  • Knudstorp, Søren Brinck (2023a). “Logics of truthmaker semantics: comparison, compactness and decidability”. In: Synthese 202. doi: 10.1007/s11229-023-04401-1.— (2023b).
    • “Modal Information Logics: Axiomatizations and Decidability”. In: Journal of Philosophical Logic 52, pp. 1723–1766. doi: 10.1007/s10992-023-09724-5.
  • Van Benthem, Johan (1996). “Modal Logic as a Theory of Information”. In: Logic and Reality. Essays on the Legacy of Arthur Prior. Ed. by J. Copeland. Clarendon Press, Oxford, pp. 135–168.— (Oct. 2017).
    • “Constructive agents”. In: Indagationes Mathematicae 29. doi: 10.1016/j.indag.2017. 10.004.— (2019). “Implicit and Explicit Stances in Logic”. In: Journal of Philosophical Logic 48.3, pp. 571– 601. doi: 10.1007/s10992-018-9485-y.

Abstract:

This report will present a preliminary attempt to explore the logical interaction between  Bimodal Logic and the Logic of Functional Dependence (LFD). LFD, proposed by Baltag and Van Benthem (2021), is an extension of classical propositional logic with local dependence formulas and dependence quantifiers. A relational semantics for LFD is established with dependence quantifiers treated as modalities and local dependence formulas treated as modal atoms. This is a good starting point for considering  Bimodal Logic, an extension of standard basic modal logic with the complement  of , proposed by Goranko (1990). We aim to address two main questions: How will LFD behave when we extend the semantics with complemental relations? What is the significance of this interaction? In this presentation, I intend to provide preliminary answers to these questions and offer some insights and results regarding these two logics.

This talk mainly relies on the works of Baltag and Van Benthem (2021) and Goranko (1990).

[1] Baltag A, van Benthem J. A simple logic of functional dependence[J]. Journal of Philosophical Logic, 2021, 50: 939-1005. 
[2] Goranko V. Completeness and Incompleteness in the Bimodal Base L(R, -R) [J]. Mathematical logic, 1990: 311-326.

Abstract:

Reason-based Obligation (RO) defines actions that individuals ought to perform based on specific objectives, rather than on norms or rules. These actions are performed instrumentally to fulfill these objectives. In natural language, this concept is typically expressed as “in order to X, you ought to do Y”. In this talk, we will extend causal models by combining the priority structure proposed by [van Benthem et al 2014] to capture the notion of RO and related reasoning. In our model, achieving the objective through an action is treated as a causal relationship between the action and the goal.

In addition, a similar priority-causality analysis of desire was proposed in [Xie & Yan 2024]. However, in our analysis, desire is interpreted through preference ordering, while obligation is interpreted through ideal ordering, highlighting their semantic differences. Therefore, we further explore the interaction between desire and RO, especially when RO is conditional on a desire. We aim to account for both the distinctions and the interconnections between these two structures.

This is a joint work with Jialiang Yan.

Reference:

  • van Benthem J, Grossi D, Liu F. Priority structures in deontic logic[J]. Theoria, 2014, 80(2): 116-152.
  • Xie K, Yan J. A logic for desire based on causal inference[J]. Journal of Logic and Computation, 2024, 34(2): 352-371.

Abstract:

A sentence in natural language can have different types of meanings. Among them, presupposition is usually characterized by being a speaker commitment in various non-assertive environments, e.g., “Did John stop smoking?” still commits to “John has smoked.” One central problem for presuppositions is how do they project from simple sentences to complex sentences, through different connectives, predicates, and quantifiers. As for binary connectives, a fundamental problem that still lacks empirical verification is whether presupposition projection is symmetric. A pioneering robust experimental study has showed that it is asymmetric for conjunction (Mandelkern et al., 2020). A following study has showed that it is symmetric for disjunction (Kalomoiros & Schwarz, upcoming). However, subtle differences in K&S’s results seem to suggest a potential confounding factor – exclusive implicature of disjunction, which has been independently brought up to solve the proviso problem (Mayr & Romoli, 2016). This talk aims to introduce relevant background on presupposition projection of disjunction (PPD) and explore the potential influence of exclusivity on the symmetry of PPD.

Major References:

  • Kalomoiros, A., & Schwarz, F. Presupposition projection from “and” vs “or”: Experimental data and theoretical implications. Journal of Semantics. Accepted
  • Mandelkern, M., Zehr, J., Romoli, J., & Schwarz, F. (2020). We’ve discovered that projection across conjunction is asymmetric (and it is!). Linguistics and Philosophy, 43(5), 473–514.
  • Mayr, C., & Romoli, J. (2016). Satisfied or exhaustified: An ambiguity account of the Proviso Problem. In M. Moroney, C.-R. Little, J. Collard, & D. Burgdorf (Eds.), Proceedings of the 26th Semantics and Linguistic Theory Conference (pp. 892–912).
  • Slides and handouts in the classes of Mingming Liu and Gennaro Chierchia

Abstract:

Intuitionistic Probability Logic ILP, which intends to provide an intuitionistic formalization of reasoning about probability, was proposed by Angelina Ilić-Stepić et al. An objective of this presentation is to introduce the logic ILP and investigate the tableau calculus for ILP. Different from the tableau given by Zoran Ognjanović, I will show a tableau without prefixes and with rules applied within the probability operators.


References

[1] Angelina Ilić-Stepić, Zoran Ognjanović, and Aleksandar Perović. “The Logic ILP for Intuitionistic Reasoning About Probability”. In: Studia Logica (2023), pp. 1–31.

[2] Zoran Ognjanović, Aleksandar Perović, and Angelina Ilić-Stepić. “Tableau for the logic ILP”. In: Publications de l’Institut Mathematique 112.126 (2022), pp. 1–11.

[3] Marcello D’Agostino et al. Handbook of tableau methods. Springer Science & Business Media, 2013.

Abstract:

Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are necessary to prove a given theorem. In this work, we systematically explore the reverse mathematics of complexity-theoretic lower bounds. We explore reversals in the setting of bounded arithmetic. Using Cook’s theory PV1 as the base theory, we show that several natural lower-bound statements about communication complexity, error-correcting codes, and Turing machines are equivalent to combinatorial principles such as the weak pigeonhole principle. Our results also yield several interesting corollaries that go against the intuition shared by some researchers in the field.
This is a joint work with Igor Oliveira (University of Warwick) and Lijie Chen (UC Berkeley).

Abstract:

In this talk, we will lift various regularity properties of analytic and co-analytic sets to universally Baire sets of reals. The notion of universally Baire sets is a generalization of the analytic and co-analytic sets introduced by Feng, Magidor, and Woodin in [F-M-W 92]. In [F-M-W 92], the authors proved that the universally Baire sets have many classical regularity properties which analytic and co-analytic sets share, such as Lebesgue measurability, the Baire property, the Bernstein property, and the Ramsey property. We will continue this line of research and show that the universally Baire sets have even more regularity properties.

Reference:
Qi Feng, M.Magidor, H.Woodin, Universally Baire Sets of Reals. In: H. Judah, W. Just, and W.H.Woodin, (eds) Set Theory of the Continuum. Mathematical Sciences Research Institute Publications, vol 26. Springer, 1992.

Abstract:

Encouraged by sabotage game and Go, I design an occupation game. We have a grid with two players who can move from one square to another, and put one line on an edge of the square where they arrive. The aim is to ‘trap’ the other player inside a totally fenced-in area. Players can make a move as one step in a compass direction (no diagonal steps allowed), where points on the boundary count as unreachable. Also in a round, a player can make one point unavailable anywhere. You lose if you are hemmed in by occupied points so cannot move when it is your turn. Occupation moves really just remove some nodes form the game board, so this can be formalized with the modal logic MLSR of point removal in van Benthem et al (2020).

Reference:
[1] Johan van Benthem, Krzysztof Mierzewski, and Francesca Zaffora Blando. The modal logic of stepwise removal. The Review of Symbolic Logic, page 1–28, 2020.

Abstract:

We introduce a modality called exclusive cover modality which requires the formulas in the prefixed multiset to be satisfied on distinct successors, and show that exclusive cover modal logic has exactly the same expressive power with graded modal logic (GML, with all the finitely-counting modalities). Also, by combining basic modal logic and exclusive cover modal logic, we get a logic which has the same expressive power with exclusive instantial neighborhood logic (eINL), together with some ideas on the axiomatization.

References
[1] De Rijke, Maarten. “A note on graded modal logic.” Studia Logica 64.2 (2000): 271-283.
[2] Fattorosi-Barnaba, Maurizio, and Francesco De Caro. “Graded modalities. I.” Studia Logica 44 (1985): 197-221.
[3] Gao, Han. “On some variants of instantial neighborhood logic.” Tsinghua University, 2022.

Sessions in 2023-2024 Fall Semester

Abstract:

《荀子》一书中广泛存在着以“凡”字为首的辩说模式。该模式是荀子论述某些重要思想主张的手段，能够从全文中被抽离出来而成为一个相对独立的辩说单元。它分别由“凡”“故”“今”等标志词所引领的句子以及与之相关的细化论证、经典引用等部分组成。各部分的句子之间有的可以形成较为严格的逻辑推理，有的则不能。本研究将在分析该模式由简至繁不同分型的基础上，探究模式各部分句子间的肌理和关系，进而准确把握《荀子》立论、辩说所依据的推理原则和逻辑观念。

Abstract:

Causality plays an important role in deontic reasoning, where the actions that individuals are obligated (permitted/forbidden) to perform are often contingent on the outcomes they bring about. This presentation explores the deontic logic with causal inferences, by proposing a causal deontic model. In this model, deontic modalities are defined in terms of causal relationships. In addition, we will discuss various deontic paradoxes and examine the dynamic aspects in this model.
This is joint work with Jialiang Yan.

Abstract:

In contemporary mathematics, a formalized and abstract language is used to define mathematical objects and to prove general theorems. Because of the close link between language and abstraction it is instructive to explore how mathematicians from different cultures theorized about language use. In my talk I will examine the case of third-century Chinese mathematician Liu Hui. His Comment- ary to the Nine Chapters on Mathematical Procedures is deeply rooted in the philosophy of his time. I argue that to Liu Hui language has two functions in mathematics. On the one hand, language can be employed to describe a situation in a mathematically fruitful way. For example, if we want to add 1⁄2 and 1/3, we can say instead that we add 3/6 and 2/6, enabling us to directly add the numerat – ors. On the other hand, language is used to make other people understand how a procedure is car- ried out and why it is correct. There can be understanding without a complete description, so the un- expressed and even inexpressible can be part of mathematical theory. In general, language is a tool to be used flexibly by the mathematician. The same situation may be described in different ways, and different situations may be described in the same way. This feature of language leads to abstract mathematical descriptions. But because understanding may go beyond words, the generality of a method does not always have to be put into abstract expressions.

Abstract:

An in-depth investigation into the internal structure of norms forms our exploration of deontic concepts such as obligation, permission and prohibition. In this paper, we offer novel perspectives for comprehending how norms constrain an agent’s behavior and for understanding deontic operators. First, we argue that norms should be conceptualized as constraints on multi-agent interactions across varied contexts. Within these situations, agents assume distinct roles or positions, their actions being shaped by the corresponding norm. Second, we propose that actions prescribed by norms in a given situation are related to the behaviors of others, whose roles are also directed by the norm. Third, based on the framework of LFD, we introduce a norm-induced dependence model and capture the formalization of the deontic operators of obligation, permission, and prohibition. Notably, our discussion on permission is inspired by the conditional independence operator in LFD. This is a joint work with Chenwei Shi and Jialiang Yan.

Abstract:

The talk explores three features of Wittgensteinian certainties, viz., their holistic character, their different levels of entrenchment, and their ability to change, and discusses the challenges posed by a formalisation of the concept of certainty with these features.

Sessions in 2022-2023 Spring Semester

Abstract:

在逻辑学的诸多应用场景中，变量之间的依赖性是一个非常普遍的现象。许多逻辑学家提出了各种不同的逻辑系统，试图形式的刻画“依赖性”这一概念，这其中包括Hintikka和Sandu提出的独立性友好逻辑（Independence Friendly Logic）、Väänänen提出的依赖性逻辑（Dependence Logic）、Baltag和van Benthem提出的函数依赖性逻辑（LFD）。本次报告将对比依赖性逻辑DL和函数依赖性逻辑LFD。这两种逻辑是非常不同的。DL是一阶逻辑的扩张，其表达力与存在二阶逻辑（existential second-order logic）等价。LFD是一阶逻辑的一个片段同时也是一种模态逻辑，所以LFD的表达力是相对受限的。判定一个DL的闭公式是否是有效式是非常复杂的，其复杂度与完整的二阶逻辑相当，因而是不可递归公理化的。但LFD有完全的形式演绎系统并且是可判定的。DL是一种非古典逻辑，排中律不是DL的有效式，但LFD是古典的。尽管如此，DL和LFD仍然具有一些共同的特征。

Abstract:

Game Theory considers about behaviour of rational agency and their optimal strategies towards their best benefit. Deontic Logic is about the reasoning of normative concepts such as obligation and permission. They looks very different seemingly. But if we consider obligation and permission respectively providing necessary and sufficient conditions for rationality in games, then we can analyze what players ought to do in a strategic game. I will focus on three deontic logics which adopting the above perspective and discuss their relationships: Van Benthem’s “Minimal Deontic Logic”, Anglberger et al.’s “Obligation as Weakest Permission”, and Trypuz and Kulicki’s “Deontic Boolean Action Logic”. Although MDL, OWP and DBAL embody the same core principle, MDL and OWP view different philosophical commitments regarding rational obligation and permission, and DBAL can be embedded into MDL. 

Abstract:

In this presentation, I will introduce an interaction between mathematical logic and probability which is a logic enriches propositional logic with a list of probability operators. As the semantics, I will introduce a class of models that combine properties of Kripke models and probabilities defined on sets of possible worlds. And the axiomatization is infinitary which contains an infinitary rule with countable many premisses and one conclusion.

Abstract:

书面文本背后的书写模式反应了人类思维的本质规律。在中国古代，文体学的诞生标志着人们开始对不同文本所反映出的不同模式划分逐渐产生自觉，刘勰、吴讷、徐师曾等理论家阐述了各自对不同文体模式的划分标准，但他们的理论停留于哲学理论阶段，并未对某种文体文章本身的内部形式结构做详细梳理。西方汉学家如瓦格纳、麦笛、耿幽静等人同样发现了中国先秦哲学文本的书写遵循着一定的模式，他们或从某一文本单元，或从文章整体来探索文本内部的形式结构和组成肌理，但他们的研究仍有很多地方需要商榷。我们的工作在古今中外成果的基础上，以《荀子·天论》作为切入点，试图对先秦“论证性”文本的典型代表《荀子》做全面的文本分析，来发现其文本内部的书写模式、组成规律以及是否具有逻辑推理。

Abstract:

函数依赖逻辑（LFD）是由Baltag和van Benthem提出的一种刻画依赖性关系的逻辑。LFD和认知逻辑之间有着紧密的联系，LFD中的算子都可以在认知逻辑中找到与之对应的认知算子。例如，LFD中的本地依赖算子对应认知逻辑中的分布式知识算子。但公共知识算子在LFD中并没有明显的对应。在这次报告中，我们将尝试给出公共知识算子在LFD框架中的解释，并通过添加公共知识算子对LFD的语言进行扩充。此外，我们会讨论扩充后的语言的表达力问题。这是与石辰威和陈谦合作的工作。

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Abstract: 

Deontic logic concerns notions such as “duty”, “permission”, and so on according to norms. Existing works primarily focus on establishing a proper logic for these notions. Nevertheless, a proper understanding of norms is seldom pursued. “What is a norm?” “How are agents’ duties and permissions derived from norms?” We believe that to come to grips with the meaning of the keyword “ought” in deontic logic, a proper understanding of these questions is unavoidable. In this talk, we confront these questions by proposing a way of understanding norms. We also make a first attempt to formalize our understanding and discuss several related issues.

Abstract:

我们将以一种全新的视角来解析奥卡姆指代模式中的上升规则。指代模式是奥卡姆人称指代理论中关于普通命题（common propositions）和分立命题（discrete suppositions）之间推理关系的子理论，包括上升（ascent）和下降（descent）两个规则。指代模式的给出是用于判定三种类型的人称指代：确定指代（determinate supposition）、周延模糊指代（distributed and confused supposition）和仅仅模糊指代（merely personal supposition）。从上世纪五六十年代起，学界涌现出一批学者，如，博纳（P. Boehner，1952）、尼尔夫妇（Kneale, William & Martha, 1962）、马修斯（G.B. Matthews, 1964，1973）、斯科特（T. K. Scott, 1966）等，尝试用现代逻辑已有成果来重新诠释指代模式，例如，将指代模式视作为词项主义逻辑的量化理论（the quantification theory of terminist logic）。然而，这些看法主要是围绕指代模式中的下降规则给出的，至于指代模式中的另一部分：上升规则，则鲜有人问津。这里，我们将借助自然逻辑单调推理的思想来重新解读指代模式中的上升规则。

Abstract:

量化模态逻辑中有从言（de dicto）和从物（de re）两种量化模态公式，而对于其中从物模态公式的语义探讨中涉及到了个体的跨世界同一问题，包括同一个体如何存在于不同的世界之中，个体与性质的关系等等。

克里普克和大卫·刘易斯各自给出了不同的语义理论，但是都使得个体的跨世界同一问题以不同的形式呈现出来。艾伦·海森（Allen Hazen）和曼弗雷德·卡普弗（Manfred Kupffer）基于对应物理论，给出了一种新的语义刻画。基于这一刻画，我们探讨克里普克和刘易斯理论中产生的问题。

Abstract: 

Numerical comparisons in natural language combine logical and arithmetical features. There have been many attempts to combine them with the language of first-order logic. However, the resulting logic is quite complex, so it is better to look into some small languages such as modal logic with counting ML(#) (see van Benthem & Icard 2021). In this talk, I will introduce the dynamic and axiomatic aspects of ML(#) by presenting several kinds of model updates that can use reduction axioms and showing that certain PDL constructions cannot be defined in the basic ML(#). I will also discuss the axiomatization of ML(#) with respect to different frame classes, including image-finite frames and arbitrary frames.

Abstract:

In this talk, we investigate dynamic modal operators containing cutting, adding and rotating, which have the ability to modify the accessibility relation of a model at both local and global levels. To begin with, we will provide motivation behind this research by exploring the connections between graph games, knowledge graphs, and social networks. We will then introduce the language and semantics used in the logic of global/local link variations, and proceed to show the axiomatization of these logics in its hybrid version, including details about its completeness proof. Furthermore, we will present our research findings on model checking and undecidability results for these logics. Finally, we will conclude by summarizing the key insights gained from our research, and suggest questions for further exploration. This is joint work with Qian Chen.

Sessions in 2022-2023 Autumn Semester

Abstract: 德国汉学家瓦格纳研究《老子》的过程中发现了中国古代哲学文本具有连锁平行式的论证模式，他以a、b标记平行的文本，以c标记分割、压缩、联结、总结a、b部分的文本。但是c部分在不同的语例中往往有不同的语法表现，并未完整具备上述功能。这些不同表现直接影响了IPS理论的严谨性和可行性，并对诸如《荀子》等论证性文本的逻辑、推理研究有所启示。

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.

Abstract:

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.

Abstract:

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. 

Abstract:

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. 

Abstract:

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.

Abstract:

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: 这篇文章介绍了一个推理社交网络内部扩散过程的一般逻辑框架。新的“社交网络中关于扩散的逻辑”是标准混合逻辑的动态扩张，并且在模型中可以包含主体的多个性质。作者为这一逻辑的静态语言和动态语言分别提供了完整的公理化，并在具体例子中展示了如何将该框架应用于具体社交网络的扩散现象。

Abstract: 在《论涵义和指称》这篇文章中，从对一个疑难的处理出发，弗雷格区分了专名的涵义和指称。进一步，弗雷格对这一区分进行的推广，认为语言中的其他类型表达式也有这一区分。本次报告分为两部分，首先考察这一区分的由来，以及在专名上的具体呈现，以及完整直陈句这一特殊专名。其次，探讨这一区分在谓词上何以实现，尤其如何理解谓词的指称——概念。

Abstract: “是”作为在传统亚里士多德逻辑和中世纪词项逻辑中都非常重要的逻辑常项，在现代逻辑中却失去了它的中心地位，其中原因可能与现代逻辑对句子的划分与传统逻辑之间有着本质的差异有关。这种传统逻辑与现代逻辑之间的差异，恰好可以通过弗雷格以及罗素等现代逻辑的创始人对包含“是”的命题所作的逻辑区分看得十分清楚。本次报告以所谓的弗雷格-罗素区分为出发点，探讨在现代逻辑中，我们该如何对“是”有一个清晰的把握。

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: 《十力语要》卷二中，熊十力在给意大利学者马格里尼的书信里谈论中国哲学的思想特点时，将“逻辑”作为理解中华文明特质和东西文化差异的一个重要切入点。熊十力在信中说：“中国哲学以重体认之故，不事逻辑，其见之著述者亦无系统。”这句话体现了熊十力的逻辑观以及对逻辑与中国哲学关系的基本认识。我们可以通过熊十力对逻辑的关注，进一步了解民国时期的文化思潮，深入探究逻辑背后的文化现象及其与中华文化的融合碰撞，并为思考新时代中华文化发展方向奠定基础。

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.

Abstract: 序提升是从一个给定集合上的序关系，提升到该集合幂集上序关系的过程。埃格利-米欧纳序是一种序提升的方式。给定一个集合的前序，可以对它的埃格利-米欧纳序进行公理化。进而，考虑一个严格版本的埃格利-米欧纳序，它可以与基于优先模型的条件句语义联系起来。非单调性在道义推理是常见的。严格的埃格利-米欧纳序定义出的条件算子的特性，使得它可以被解释为“条件应该”，从而处理一些道义悖论。

Abstract: “侔”是墨家“辟、侔、援、推”四种论证形式之一，出自《墨经·小取》篇。《小取》在论述“侔”时，提出了诸多悖论，比如“获，人也；爱获，爱人也”；“其弟，美人也，爱弟，非爱美人也”。前者推论有效的原因，与隐藏在动宾短语中的存在量词有关，其底层的逻辑推论形式为右侧向上单调推理。而后者的谬误成因，则是由于动宾短语中位于宾项位置的量词为全称量词，它会为动宾短语提供单调向下的推理环境。

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