Events in 2024-2025 Fall Semester
Abstract:
Non-wellfounded and cyclic proofs provide a formal counterpart to proofs by infinite descent. So, proofs of this kind are helpful for logics dealing with inductive (and coinductive) definitions. This includes systems of arithmetic (induction over the natural numbers) and modal logics with fixed points (common knowledge and temporal operators). In this talk, I will introduce non-wellfounded and cyclic proofs and study their proof-theoretic properties.
Abstract:
当前,人工智能技术的飞速发展深刻的影响着社会变革,在赋能千行百业的同时,也为社会科学领域带来了前所未有的机遇。尤其是以大模型为代表的生成式人工智能展现出了强大的能力,这些技术不仅在社会科学的理论研究中开辟了新领域,还为解决复杂社会问题提供了新的工具。本次报告,将从人工智能、哲学、传播学等跨学科视角来探讨人工智能前沿技术、行业最新的典型应用,以及其中带来的安全和伦理问题,旨在引起大家的讨论,启发对于人工智能前沿技术向前的想象力和向后的反思力。
Abstract:
We provide a semantics for a language containing indicatives and epistemic modals, which are elusive in formal semantics. The main idea is to evaluate a formula at a world in a context. An indicative is true at a world in a context if its consequent is true at the world in the new context updated by its antecedent in the old context. An epistemic necessity is true at a world in a context if it is true at all worlds in the context. Armed with the semantics, we define a ternary notion of validity, by which an inference is not valid per se, but valid under a set of assumptions, which are used to specify the context. The ternary notion of validity is meant to give a unified solution to several puzzles concerning indicatives and epistemic modals.
Abstract:
The Infinite Ramsey Theorem states that given positive integers m and r, given a coloring of all m-element subsets of the natural numbers into r colors, there is an infinite set of natural numbers such that all of its m-element subsets have the same color. Following Sierpinski’s work in the 1930’s on colorings of finite linear orders as subsets of the rationals, the area of big Ramsey degrees seeks to understand when and to what extent the Infinite Ramsey Theorem extends to infinite structures. This talk will introduce big Ramsey degrees, demonstrate known characterizations, and discuss methods from set theory and computability applied in their study.
Abstract:
Many members of the crowd of modern logical systems look very different qua syntax and semantics, but how much unity is there when we look ‘under the hood’ of their engines? I start with some significant examples of translation and other forms of reduction between logical systems, some obvious, some quite surprising. As a special interest item, I will discuss ‘tracking’ of dynamic updates in different logics, taking the case of logics for analyzing games as a running example.
Reference:
- J. van Benthem, ‘Implicit and Explicit Stances in Logic’, Journal of Philosophical Logic, 2018, https://pure.uva.nl/ws/files/85565602/Benthem2019Article_ImplicitAndExplicitStancesInLo.pdf
- J. van Benthem, ‘Tracking Information’, in K. Bimbó, ed., Michael Dunn on Information–Based Logics, Springer, Dordrecht, 363–389.
- J. van Benthem, ‘Game levels, Game logics, Translations, Tracking, and More’, working paper, ILLC, University of Amsterdam.
Abstract:
Polymodal provability logic GLP is incomplete w.r.t. Kripke frames. It is known to be complete w.r.t. topological semantics, where the diamond modalities correspond to topological derivative operations. However, the topologies needed for the completeness proof are highly non-constructive. The question of completeness of GLP w.r.t. natural scattered topologies on ordinals is dependent on large cardinal axioms of set theory and is still open. So far, we are lacking a useable class of models for which GLP is complete.
In this paper (joint work with Yunsong Wang) we define a natural class of countable general topological frames on ordinals for which GLP is sound and complete. The associated topologies have been introduced by Thomas Icard in 2011. In addition, we specify a suitable algebra of subsets of an ordinal closed under the boolean and topological derivative operations. These algebras are based on the notion of a periodic set of ordinals generalizing that of an ultimately periodic omega-word.
We review the history and some recent work on what is known since the 1990s as distributed knowledge. Such epistemic group notions are currently getting more and more attention both from the modal logical community and from distributed computing, in various settings with communicating processes or agents. The typical intuition is that if a knows p, and b knows that p implies q, then together they know that q: they have distributed knowledge of q. In order to get to know q they need to share their knowledge. We will discuss: (i) the complete axiomatization, (ii) why not everything that is distributed knowledge can become common knowledge, (iii) the notion of collective bisimulation, (iv) distributed knowledge for infinitely many agents, (v) the novel update called resolving distributed knowledge and some variations (and its incomparable update expressivity to action models), (vi) distributed knowledge that is stronger than the sum of individual knowledge (where the relation for the group of agents is strictly contained in their intersection), (vii) common distributed knowledge and its topological interpretations, (viii) dynamic distributed knowledge, a version of the semantics ensuring that what is distributed knowledge becomes common knowledge, and the axiomatization, expressivity and bisimulation characterization of this logic.
Early language acquisition research provides a unique perspective to understanding how children acquire language. One question concerns when children display specific abstract linguistic knowledge early in development. The other is how children break into a particular language (i.e. their mother tongue), assuming the availability of innate linguistic knowledge like Universal Grammar. In this talk, I will report some young children’s perception and comprehension findings that attempt to provide answers to these important questions from a perspective of L1 acquisition of Mandarin Chinese. I will focus on Mandarin-learning toddlers’ syntactic categorization, distinction of differing verb types and processing of function words, trying to show their early sensitivity to very subtle syntactic and semantic aspects of linguistic forms and structures.
Events in 2023-2024 Spring Semester
Abstract:
My talk will explore a common foundation for mathematical reasoning and for their underlying cognitive processes. Starting from counting and spatial reasoning as two core developmental domains of mathematical cognition, I will discuss how the notion of object can be characterized by “concept lattice” (as in Formal Concept Analysis of Ganter and Wille 1999), and how the structure of knowledge can be captured by “knowledge space” (and its learning space, by Doignon and Falmagne 2015). Finally, motivated by the intertwined relations among lattice, logic, and topology, I will describe how the suite of topological operators, and hence topological semantics, can be generalized to general set systems (Lei and Zhang 2019), paving the way for using the latter as the common core for mathematical/formal cognitive systems.
Abstract:
I defend the negative answer to the question in the title, “Is logic aziomatizable?”, by considering sentences that involve plural constructions, such as the following:
[A] There are some things each of which admires one of them.
[B] There are some critics who admire only one another.
We can intuitively see that [A], for example, is logically implied by infinitely many sentences, such as the following:
[A1] c1 admires c2.
[A2] c2 admires c3.
…
[An] cn admires cn+1.
…
But [A] is not logically implied by any finite number of sentences among these. So the logic of languages that are rich enough to include [A] is non-compact. It follows from this that the logic of such languages is not axiomatizable. Similarly, we can see that [B], known as the Geach-Kaplan sentence, is logically implied by the following sentences (but not by any finite number of them):
[A1] c1 admires only c2, c1 is not c2, and c1 is a critic.
[A2] c2 admires only c3, c2 is not c3, and c2 is a critic.
…
[An] cn admires only cn+1, cn is not cn+1, and cn is a critic.
…
So we can conclude that the logic of languages that include [B] is not axiomatizable.
To put the argument in proper perspective, I shall discuss contemporary account of plural constructions and suggest that they fail to do justice to the logic of plural constructions because they are based on the traditional view of plural constructions as devices for abbreviating singular constructions. And I shall give a sketch of my account of the logic of plural constructions that are based on the view of plurals as substantial devices that complement their singular cousins.
Abstract:
逻辑是刻画程序语义的基础。可满足性模理论(SMT)求解器是许多程序分析与验证技术的推理引擎。目前,存在多种一阶理论,例如线性算术理论、数组理论、位向量理论、未解释函数理论等,基于这些理论已经能够很好的支持串行程序验证。然而,却缺乏直接面向并发程序验证的一阶理论。本报告介绍我们在并发程序逻辑理论方面取得的最新研究成果,并介绍相应的自动判定算法和程序验证工具。基于该理论开发的并发程序验证工具Deagle连续三年获得国际软件验证大赛并发安全赛道冠军。
Abstract:
Conditionals in their different flavors—material, strict, indicative, counterfactual, probabilistic, constructive, quantum, etc.—have long been of central interest in philosophical logic. In this talk, we will discuss our recent work on a new semantics for conditionals, covering a large class of what we call preconditionals. Familiar examples of bounded lattices equipped with a preconditional include Heyting algebras, ortholattices with the Sasaki hook, and Lewis-Stalnaker-style conditional algebras satisfying the so-called Flattening axiom. We have shown that every bounded lattice equipped with a preconditional can be represented using a relational structure (suitably topologized), yielding a single relational semantics for conditional logics normally treated by different semantics, as well as generalizing beyond those semantics. An associated paper is available at https://arxiv.org/abs/2402.02296.
Abstract:
推理是传统人工智能中的重要研究方向,取得了很多成果。机器学习是当前人工智能研究的重要方向,特别是深度学习方法展现出强大的学习能力。在这个报告中,我们从一些实际应用问题开始,讨论学习和推理结合的实际需求,探讨这一研究方向的不同解决思路和关键问题。
Abstract:
Continuous logic is a nonstandard multi-valued logic developed in recent years to study metric structures. In this talk we consider the question whether universal structures with the Urysohn property exist in continuous logic. It turns out that the answer depends on some particular properties of the continuous signatures. In this talk I will give conditions that will completely characterize the existence of Urysohn structures and some other related properties in continuous logic. This is joint work with Xuanzhi Ren.
Events in 2023-2024 Fall Semester
Abstract:
Questions are a quintessential interface phenomenon. Many (most?) languages use syntactic cues to separate declaratives and interrogatives; all languages distinguish interrogatives from declaratives semantically; all languages impose pragmatic requirements for the felicitous use of questions (calibrated to the type of question involved); most languages indicate questions vs. assertions prosodically, even if it may be hard to correlate each question type with a unique prosodic profile. These aspects of questions are clearly present in matrix questions but to what extent they are also present in embedded questions depends on the type of embedding involved: quoted interrogatives, quasi-subordinated interrogatives, fully subordinated interrogatives. I probe the interfaces between syntax, semantics, pragmatics and prosody in matrix as well as embedded questions, approaching the issue through the perspective of a three step process of question formation at the left periphery of the interrogative clause.
Abstract:
There are many algorithms implicit or explicit in the way society works: for example, an election, or vaccine distribution policy. These algorithms rely on logical properties of underlying physical and social structures. For instance, in an election, we not only want confidentiality but also verifiability (that every vote cast has been counted), and many more such properties. Can we prove that these requirements are even consistent (something that we take for granted)?
Abstract:
This study focuses on the so-called pseudo-possessive construction in Chinese, which typically refers to such sentences as Ta-de(his) laoshi(teacher) dang-de(act-De) hao(well) ‘He acts well as a teacher’. In this kind of construction, within the subject of the verb, ta-de laoshi ‘his teacher’, the possessor and the possessee never form a possessive reading. Rather, they perform as subject and object respectively. Many analyses are proposed to explain such a syntax-semantics mismatch. For instance, in the formal syntactic framework, previous studies attribute the pseudo-possessive reading to a syntactic reanalysis or a verb movement. However, the present study argues against these syntactic derivational approaches, and proposes that possessive construction can itself encode an event reading. In other words, the ability of encoding events is the intrinsic property of nominal structure, which does not need the assistance of verbs. In the possessive construction, the possessor is in fact an argument of a nominal predicate. Furthermore, the pseudo-possessive construction in Chinese is attributed to the following three factors: the subject of the V-de construction encodes an event, the predicate following V-de describes the property of the event subject, the verb affixed by -de is the externalization of the way in which the subject satisfies the predicate.
Abstract:
Intuitionistic tense logic (IK.t), in the sense of W. B. Ewald, is obtained by adding two pairs of adjoint tense operators (F, H) and (P, G) to intuitionistic logic. It can be seen as a counterpart of classical tense logic in the setting of intuitionistic logic. The decidability of IK.t is still open. In this talk, I will consider the natural algebraic semantics of the disjunction-free fragment of IK.t and the {\wedge,\vee,\neg,F,H,P,G,0}-reduct of IK.t firstly, and then introduce cut-free Gentzen calculi for these two fragments. Finally, using methods from algebraic proof theory, I will show that both of these two fragments have the FMP and whence they are decidable. This work is joint with Zhe Lin.
Abstract:
In this talk, we study a bimodal logic over neighborhood structures with two normal unary modalities. As first proposed by Zhao (2021), the language is defined via a simultaneous induction of two types of formulas, point-formulas and set-formulas, to be evaluated on possible worlds and sets of worlds respectively. We show that the bimodal language is equally expressive as the language of instantial neighborhood logic proposed by van Benthem et al. (2017). As the main result, we give a sound and strongly complete Hilbert axiomatization featuring two intertwined normal K-like systems with “bridging rules”, where a proof for a point-formula can be a mixed sequence of both point- and set-formulas. As a corollary, we show that the instantial neighborhood logic is compact, thus solving an open problem in the literature.
Events in 2022-2023 Spring Semester
Abstract:
I will present joint work with A. Baltag on modelling scenarios in which agents read or communicate (or somehow gain access to) all the information stored at specific sources, or possessed by some other agents (including information of a non-propositional nature, such as data, passwords etc). Modelling such scenarios requires us to extend the framework of epistemic logics to one in which we abstract away from the specific announcement and formalize directly the action of sharing ‘all you know’ (with some or all of the other agents). In order to do this, we introduce a general framework for such informational events, that subsumes actions such as ‘sharing all you know’ with a group or individual, giving one access to some folder or database, hacking a database without the owner’s knowledge, etc. We formalize their effect, i.e. the state of affairs in which one agent (or group of agents) has ‘epistemic superiority’ over another agent (or group). Concretely, we express epistemic superiority using comparative epistemic assertions between individuals and groups (as such extending the comparison-types considered in [5]). Another ingredient is a new modal operator for ‘common distributed knowledge’, that combines features of both common knowledge and distributed knowledge, and characterizes situations in which common knowledge can be gained in a larger group of agents (formed of a number of subgroups) by communication only within each of the subgroups. We position this work in the context of other known work such as: the problem of converting distributed knowledge into common knowledge via acts of sharing [4]; the more semantic approach in [2] on communication protocols requiring agents to ‘tell everybody all they know’; the work on public sharing events with a version of common distributed knowledge in [3]; and the work on resolution actions in [6].
[1] A. Baltag and S. Smets, Learning what others know, in L. Kovacs and E. Albert (eds.), LPAR23 proceedings of the International Conference on Logic for Programming, AI and Reasoning, EPiC Series in Computing, 73:90-110, 2020. https://doi.org/10.29007/plm4
[2] A. Baltag and S. Smets, Protocols for Belief Merge: Reaching Agreement via Communication, Logic Journal of the IGPL, 21(3):468-487, 2013. https://doi.org/10.1093/jigpal/jzs049
[3] A. Baltag, What is DEL good for? Lecture at the ESSLLI2010-Workshop on Logic, Rationality and Intelligent Interaction, 16 August 2010.
[4] J. van Benthem, One is a lonely number. In P. Koepke Z. Chatzidakis and W. Pohlers, (eds.) Logic Colloquium 2002, 96-129, ASL and A.K. Peters, Wellesley MA, 2002.
[5] H. van Ditmarsch, W. van der Hoek & B. Kooi, Knowing More – from Global to Local Correspondence, Proc. of IJCAI-09, 955–960, 2009.
[6] T. Agotnes and Y.N. Wang, Resolving Distributed Knowledge, Artificial Intelligence, 252: 1–21, 2017. https://doi.org/10.1016/j.artint.2017.07.002
Abstract:
In this talk, I will first demonstrate the internal antisymmetry of Chinese disyllabic coordinative verbs (CDCVs) such as \zhi-zao/ ‘manufacture’ and \xiu-li/ ‘repair’. Using a sample of 400 CDCVs and a carefully designed annotation scheme to analyze all the CDCVs, we find that for each of the 400 CDCVs, one of the two root morphemes inside the compound verb can be identified as the more prominent one (call it H), which plays a more important role than the other root morpheme in determining the argument structure of the compound verb. This means that the 400 CDCVs have an asymmetrical internal structure with its two root morphemes being unequal in function. By studying the properties of all the Hs, we find strategies employed by the grammar to decide H, and provide an account for the strategies. Relying on our empirical findings about the internal antisymmetry of CDCVs, I then discuss and try to explain two theoretical issues. The first is about a well-known generalization in Chinese linguistics, namely that disyllabic verbs exhibit nominal behavior which corresponding monosyllabic verbs lack. The other is about the peculiar fact that CDCVs exist in large amount in Chinese whereas other languages like English rarely have equivalents.
Abstract:
Dependence logic was introduced by Väänänen (2007) as a novel formalism for reasoning about dependence and independence relations. The logic adopts the team semantics of Hodges (1997). The basic idea of team semantics is that dependency properties can only manifest themselves in multitudes, and thus formulas of dependence logic are evaluated on sets of assignments (called teams) instead of single assignment as in the usual Tarskian semantics. A team can be naturally viewed as a relational database, a dataset, an information state, etc. Thanks to the simple structure of teams and the abundance of their interpretations in various fields of science, team semantics and dependence logic have recently found a number of applications in addressing issues in database theory, formal linguistics, quantum foundations, social choice and so on. In the first part of this talk, I will provide an overview of the core theory and applications of dependence logic. Teams are essentially relations, which are second-order objects. Dependence logic is known to be equivalent to existential second-order logic, and thus cannot be effectively axiomatized in full. In the second part of the talk, I will survey some recent developments in finding partial axiomatizations for dependence logic.
Speaker’s homepage: https://sites.google.com/site/fanyanghp/
Abstract:
This talk will introduce my recent book Studies in No-Self Physicalism. I will first explain the basic ideas of ‘no-Self’ physicalism. This introduces the basic assumptions and overall goal of the researches presented in this book and introduces chapters 1 and 2 of the book. Chapters 3 to 8 of the book develop a series of philosophical theories under the framework of No-Self Physicalism. They include theories on concept and conceptual representation (Chapter 3), thought, truth, analyticity, belief ascription, and modality (Chapter 4), philosophy of mathematics (Chapter 5), epistemic justification, knowledge, apriority, and intuition (Chapter 6), physicalistic ontology (Chapter 7), and coherent formulation of physicalism (Chapter 8). This talk will also very briefly introduce some of the ideas in these chapters.
Speaker’s homepage – http://cnu-cn.academia.edu/FengYe
Abstract:
金岳霖系统地分析了真之符合论中的“符合”,认为“符合是‘真’底所谓”,融洽、有效和一致是经验到符合的标准,它们都是真之标准。在金岳霖的理论中,符合论最为关键的成分“符合直观”被解释为符合感。符合感在横的时间上就是符合,但就纵的时间说,符合感与符合不必合一,即判断的对与命题的真不必合一。金岳霖关于“符合”的分析回应了符合论的核心问题“符合是什么”,这个问题在当前文献中也被称为“刘易斯—海德格尔问题”。
The problem of no hands concerns the existence of so-called responsibility voids: cases where a group makes a certain decision, yet no individual member of the group can be held responsible for this decision. Criteria-based collective decision procedures play a central role in philosophical debates on responsibility voids. In particular, the well-known discursive dilemma has been used to argue for the existence of these voids. But there is no consensus: others argue that no such voids exist in the discursive dilemma under the assumption that casting an untruthful opinion is eligible. We argue that, under this assumption, the procedure used in the discursive dilemma is indeed immune to responsibility voids, yet such voids can still arise for other criteria-based procedures. We provide two general characterizations of the conditions under which criteria-based collective decision procedures are immune to these voids. Our general characterizations are used to prove that responsibility voids are ruled out by criteria-based procedures involving an atomistic or monotonic decision function. In addition, we show that our results imply various other insights concerning the logic of responsibility voids.
Reference available at https://biblio.ugent.be/publication/8735886
Abstract:
Strategic reasoning is usually performed in specific strategy contexts, concerning which strategies are in consideration. Strategic reasoning can involve the change of strategy contexts. In this talk, we present a logic for strategic reasoning involving the change of strategy contexts caused by commitments to strategies. The logic has two featured formulas: (1) for some strategy of an agent compatible with the strategy context, if the agent commits to it, a formula is guaranteed to be true; (2) for every strategy of an agent compatible with the strategy context, if the agent commits to it, a formula is guaranteed to be true. Commitments to strategies shrink strategy contexts, which are defined as sets of sets of individual strategies.
This talk is based on a joint work with Valentin Goranko from Stockholm University.
Abstract:
This talk is a survey of a project of my research since around 2014. First, I will introduce the aim, the paradigm and the approaches in mathematical foundations of quantum theory which form the background of this talk. Second, I will introduce a toy model of the kind of mathematical structure which I use to model the states of a quantum system and the orthogonality relation between them. Third, I will discuss the way to describe quantum measurement and quantum entanglement only in terms of the orthogonality relation. We will see that such a simple description highlights some essentials and provides some insights.
Abstract:
The epistemic modals ‘might’ and ‘must’ have peculiar logical features that are challenging to account for in a broadly classical framework. In this talk, I will discuss a non-classical approach to epistemic modals from my paper with Matthew Mandelkern, “The Orthologic of Epistemic Modals” (https://escholarship.org/uc/item/0ss5z8g3), with special attention to the new Section 5 (“Constructing possibilities from worlds”).
In distributed games, every player sees only the local game arena, and announces potential joint moves with other players. The global arena resolves these and the game proceeds. We propose a two-level logic to reason in such games, with one layer of local formulas for each player, and the global formulas. We present a complete axiom system for valid formulas and show decidability.
This talk is based on joint work with Lei Li, Fenrong Liu and R. Ramanujam.
Abstract:
Reasoning about information, its potential incompleteness, uncertainty, and contradictoriness need to be dealt with adequately. While incompleteness and uncertainty are typically accommodated within one formalism, e.g. within various models of imprecise probability, contradictoriness and uncertainty less so — conflict or contradictoriness of information is rather chosen to be resolved than to be reasoned with. To reason with conflicting information, positive and negative support — evidence in favour and evidence against — a statement are quantified separately in the semantics. This two-dimensionality gives rise to logics interpreted over twist-product algebras or bi-lattices, the well known Belnap-Dunn logic of First Degree Entailment being a prominent example. Belnap-Dunn logic with its double-valuation frame semantics can in turn be taken as a base logic for defining various uncertainty measures on de Morgan algebras, e.g. Belnapian (non-standard) probabilities or belief functions.
In spirit similar to Belnap-Dunn logic, we have introduced many-valued logics suitable to reason about such uncertainty measures. They are interpreted over twist-product algebras based on the [0,1] real interval as their standard semantics and can be seen to account for the two-dimensionality of positive and negative component of (the degree of) belief or likelihood based on potentially contradictory information, quantified by an uncertainty measure. The logics presented in this talk include expansions of Łukasiewicz with a de-Morgan negation which swaps between the positive and negative semantical component.
Our main objective is to utilise apparatus of two-layered logics to formalise reasoning with uncertain information, which itself might be non-classical, i.e., incomplete or contradictory. Many-valued logics with a two-dimensional semantics mentioned above are used on the outer layer to reason about belief, likelihood or certainty based on potentially incomplete or contradictory evidence, building on Belnap-Dunn logic as an inner logic of the underlying evidence. This results in two-layered logics suitable for reasoning scenarios when aggregated evidence yields a Belnapian probability measure or a belief function on a De Morgan algebra.
(This talk is rooted in joint work with S. Frittella, D. Kozhemiachenko, O. Majer and S. Nazari.)
Abstract:
In this talk, I will present some results from the study of transitive logics of finite depth and finite suc-eq-width. They are logics in NExtK4 containing the standard depth axioms and the suc-eq-width axioms, which are generalizations of the standard width axioms. The frame condition for a suc-eq-width axiom requires, in a rooted transitive frame, a finite upper bound of cardinality for antichains of points with different sets of proper successors. Our first result demonstrates that all these logics are finitely axiomatizable, thereby generalizing Rybakov and Chagrov’s result of the finite axiomatizability of extensions of S4 of finite depth and finite width. Applying the well-known result from Segerberg that all transitive logics of finite depth have the finite model property, we then establish that all transitive logics of finite depth and finite suc-eq-width are decidable. Lastly, the complexity of the satisfiability problem for these logics can be shown to fall within the NP class.
Practical knowledge, in the sense made famous by G. E. M. Anscombe, is “the knowledge that a man has of his intentional actions”. This knowledge is very ordinary, but philosophically it is far from easy to understand. One illuminating approach to practical knowledge is to see it as a species of self-knowledge or self-consciousness. I offer an enrichment of this approach here, by exploiting Gilbert Ryle’s discussion of heeding (that is, paying attention), in particular paying attention to one’s own intentional action. I will argue, in a broadly Kantian spirit, that paying attention to what one is doing is an exercise of practical self-consciousness. It is how practical self-consciousness is “schematized”.
Events in 2022-2023 Autumn Semester
Abstract:
量子力学奠定了现代科学的基础,成功地推动当代技术革命方面。然而,对于量子力学诠释——理解波函数如何述刻画微观世界,迄今为止人们并未形成共识。本报告将结合报告人二十余年关于量子力学基础问题艰辛探索,简要介绍和评述这些量子力学诠释的基本思想、它们之间的逻辑关系及其实验检验的可能性。报告强调,首先要明确定义什么是量子测量、什么是量子测量的客观性,才能澄清量子力学诠释中的一些基本概念,避免量子观念滥用引起的意识论上的问题、使得量子技术发展误入歧途。
报告着重阐述了量子力学如何描述微观世界的客观属性。我们认为,由于采用了不具唯一性的波包塌缩假设,哥本哈根诠释对哲学基本问题构成的挑战并非根本性的,有人由此得到物质-意识不可分的结论在科学和哲学都是不严谨的。针对卡尔·波普尔“三个世界”哲学,报告基于量子测量 理论描述了多个观察者如何对微观系统进行探测,形成客观的量子测量,产生微观世界的客观知识,从而对 波普尔的客观知识世界(世界 3)给出了基于量子力学本体论的哲学解读:物质世界(世界 1)与精神感知世 界(世界 2)的物化载体(认识主体)相互作用,形成二者的关联和纠缠,它们对应了主观世界在内的精神 感知全体,其中具有客观性的部分构成了微观世界的客观知识。文章还指出,伴随着微观系统客观知识世界 的形成,信息从物质世界流向主观客体,信息流的指向定义了不同于通常物质世界的精神感知的物化载体。
Abstract:
1885 年,也就是弗雷格的 《算术基础》 出版一年后,康托发表了他对这部著作的评论。 这篇评论只有一页,但涉及一个非常重要也非常有趣的问题,那就是概念外延和集合哪一个更为基础。在本次演讲中,我们试图讨论这一分歧的哲学意义极其所代表的不同传统,并且将可定义性视为把握客观概念的主要工具。我们会论证康托的评论和弗雷格两个月后的回应不仅具有重大的历史意义,而且与当今数学基础的一个重大问题密切相关。 集合论虽然自康托尔以来取得了巨大的成功,但其基础所面临的困难可能与康托对概念的误解有关。这些困难借助弗雷格和哥德尔的概念论哲学思想有可能找到数学解决方案。
Abstract:
The development of systems of paraconsistent, inconsistency-tolerant logics in the 20th century can be seen as a major and bold move in the history of ideas. Ever since Aristotle’s formulation of the law of non-contradiction, when he wrote in 1011b13–14 of what is now called Metaphysics IV that “opposite assertions cannot be true at the same time,” negation consistency has been regarded as absolutely indispensable for theoretically rational theory formation. However, even the founders of paraconsistent, inconsistency-tolerant logic, Stanislaw Jaskowski and Newton da Costa, and the key proponent of dialetheism, Graham Priest, did not liberate themselves completely from the consistency bonds of classical logic and the most prominent non-classical logics in more than one way, especially in not accounting for logically provable (or, semantically, logically valid) contradictions and non-trivial negation inconsistent logics.
I will suggest to radically break with the time-honored Aristotelean tradition of complete banishment of contradictions in science. In particular, I will argued that it is theoretically rational to believe not only that there exist interesting or important non-trivial negation inconsistent theories but also that there exist interesting or important non-trivial negation inconsistent logics. I will present several examples of such logics.
Abstract:
Game theorists have proposed backward induction as the reasoning procedure that rational players follow in turn-taking games. An alternative is forward induction, in which a player rationalizes any previous move by the opponent that does not fit backward induction. Do adult participants’ choices in centipede-like turn-taking games fit better with backward or forward induction? In a couple of experiments, participants played a turn-taking game against a computer, which was programmed to deviate often from the backward induction strategy at the beginning of the game. Participants had been told that the computer was optimizing against some belief about the participant’s future strategy. In the course of the experiments, participants were asked questions about their own and the opponent’s reasoning at all decision nodes of a sample game. We checked how their verbalized strategies fit to their choices in the experimental games. Although in the aggregate, participants tend to favor the forward induction choice, their verbalized strategies usually involve explicit theory of mind, their own attitudes towards risk, and those they assign to the opponent, as well as considerations about cooperativeness.
This talk is based on joint work with Aviad Heifetz, Rineke Verbrugge and Harmen de Weerd.
Abstract:
Epistemic logics are traditionally about the modalities ‘belief-that’ and ‘knowledge-that’. The talk will instead focus on modalities of the ‘knowledge-whether’ kind, providing insights about the principles governing common knowledge and about the interplay between knowledge and belief. As ‘belief whether’ does not exist in natural language we use the term ‘belief about’ instead. Concerning common knowledge, we study the following principle for common knowledge: common knowledge that each agent knows whether p implies common knowledge whether p. If the logic of knowledge is S5 then it provides an equivalent and more intuitive alternative to the standard induction axiom for common knowledge. Concerning the interplay between knowledge and belief we follow, among others, Lenzen and Voorbraak and adopt S4.2 as the logic of knowledge and KD45 as the logic of (strong) belief, plus the interaction axioms ‘knowledge implies belief’, ‘belief implies knowledge to believe’, and ‘belief implies belief to know’. In this framework we study the two modalities ‘true belief about’ andmere ‘belief about’: they lead to an elegant characterisation of epistemic-doxastic situations as well as to the definition of interesting lightweight fragments of epistemic-doxastic logic.
References:
- Andreas Herzig, Elise Perrotin: True Belief and Mere Belief About a Proposition and the Classification of Epistemic-Doxastic Situations. Filosofiska Notiser, 103-117 (2021) http://filosofiskanotiser.com/Herzig_Perrotin.pdf
- Andreas Herzig, Elise Perrotin: On the Axiomatisation of Common Knowledge. AiML 2020: 309-328. http://www.aiml.net/volumes/volume13/Herzig-Perrotin.pdf
- Martin C. Cooper, Andreas Herzig, Faustine Maffre, Frédéric Maris, Elise Perrotin, Pierre Régnier: A lightweight epistemic logic and its application to planning. Artif. Intell. 298: 103437 (2021)
Abstract:Individual rationality plays a central role in modern economic theory, while how to measure rationality has been quite challenging. In particular, whether the rationality measured in different domains is stable or not is an open question. Combining consumers’ purchase data from a large supermarket chain and their choice in a survey experiment, we directly examine three important questions for rationality measurements: (1) external validity: can rationality measured in the survey experiment successfully predict consumers’ actual purchase behavior; (2) cross validity: is rationality exhibited in risk preference consistent with that in social preference? (3) time stability: does an individual’s rationality level vary with time windows?
Abstract:
讲座以结构平衡逻辑为例介绍非信息因素驱动的社会网络更新模型和逻辑学研究视角,并解释此类工作中常常面临的一些技术难题,顺带介绍报告人在这个领域的近期工作和研究想法。
参考文献:王轶,《逻辑、博弈与计算——社会网络平衡研究》。
Abstract:
This talk establishes the Craig interpolation theorem of bi-intuitionistic stable tense logic BiSKt, which is proposed by Stell et al. (2016). First, we define a sequent calculus G(BiSKt) with the cut rule for the logic and establish semantically that applications of the cut rule can be restricted to analytic ones, i.e., applications such that the cut formula is a subformula of the conclusion of the cut rule. Second, we apply a symmetric interpolation method, originally proposed by Mints (2001) for multi-succedent calculus for intuitionistic logic, to obtain the Craig interpolation theorem of the calculus G(BiSKt). Our argument also provides a simplification of Kowalski and Ono (2017)’s argument for the Craig interpolation theorem of bi-intuitionistic logic. This is joint work with Hiroakira Ono (JAIST).
Abstract:
It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. For modal logics, limit behavior for models and frames may differ. In 1994, Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5. They also proposed zero-one laws for the corresponding classes of frames, but their zero-one law for K-frames has since been disproved, and so has more recently their zero-one law for S4-frames.
In this talk, we prove zero-one laws for provability logic with respect to both model and frame validity. Moreover, we axiomatize validity in almost all irreflexive transitive finite models and in almost all irreflexive transitive finite frames, leading to two different axiom systems. In the proofs, we use a combinatorial result by Kleitman and Rothschild about the structure of finite (strict) partial orders: almost all of them consist of only three layers. Finally, we present empirical results in order to give an idea of the number of elements from which onwards a formula’s almost sure validity or almost sure invalidity stabilizes in such three-layer Kleitman-Rothschild frames. We also discuss possible extensions of the zero-one laws to the modal logics S4 and K4.
Abstract:The standard theory of belief revision—the AGM theory—has long been challenged with some putative counterexamples, and its defenders often reply by (explicitly or implicitly) following a quite general, powerful strategy. I will describe that reply strategy in detail before I undermine it. More specifically, I will give a class of counterexamples to the AGM theory (and anything stronger) for which the reply strategy no longer works. Worse, my counterexamples are pervasive in science, in the sense that statistical hypothesis testing is pervasive in science. Some weakenings of the AGM theory will then be considered, and their prospects will be assessed (optimistically). I will close by sketching how all this fits into the bigger picture of scientific inference that I defended elsewhere (in the 2022 PSA). If I am right, belief revision theory, when done right, is an important missing part of a good philosophy of statistics.
Abstract:In this talk, we examine the limit of the first incompleteness theorem (G1). Goedel-Rosser first incompleteness theorem claims that any consistent recursively axiomatized extension of PA is incomplete. The notion of interpretation provides us a method to compare different theories in distinct languages. We can generalize G1 via the notion of interpretation in an abstract way. For a consistent RE theory T, we define the notion “G1 holds for T”. We examine the question: are there minimal theories for which G1 holds. The answer of this question depends on how we define the notion of minimality. We first review some known results of this question in the literature based on different notions of minimality. Then we examine the question: are there minimal theories for which G1 holds with respect to interpretation. We know that G1 holds for essentially undecidable theories. Effectively inseparable (EI) theories are much stronger than essentially undecidable theories, and G1 holds for EI theories. A natural question is: are there minimal EI theories with respect to interpretation? We negatively answer this question and prove that there are no minimal effectively inseparable theories with respect to interpretation: for any EI theory T, we can effectively find a theory which is EI and strictly weaker than T with respect to interpretation. We give two different proofs of it. Finally, if time allows, we give a brief discussion of the limit of the second incompleteness theorem.
Abstract:
There are various negative translations from classical propositional logic (CPL) into intuitionistic propositional logic (IPL). Glivenko’s double negation translation is one of the fundamental negative translations from which other embeddings are derived. In this lecture, we sketch the algebraic, semantical and proof-theoretic methods for proving Glivenko’s embedding of CPL into IPL. After a short look back to the Glivenko type theorems for intuitionistic modal logics, we introduce recent work on negative translations, including the Kolmogorov, Goedel-Gentzen and Kuroda, for intuitionistic tense logics based on Ewald’s logic IKt. We show a new cut-free sequent calculus for IKt, and then by the proof-theoretic method, we show that the three types of negative translation embedding hold for intionistic tense logics which are axiomatizable by strictly positive formulas. Finally we give a new characterization of Glivenko type theorem for intuitionistic tense logics.
Events in 2021-2022 Spring Semester
Abstract:
The notion of a nonstandard model was introduced by Skolem almost 90 years ago. Since then, nonstandard models have been a subject of study in mathematical logic. In recent years, such structures were successively used to investigate combinatorial problems in reverse mathematics. This talk will give a brief introduction of the key features of a nonstandard model, provide some examples, and discuss the role of nonstandard models in metamathematical investigations, as well as in the philosophy of mathematics.
Abstract:The talk is divided into two parts: the first part gives a brief introduction to the topological duality between Boolean algebras with operators and descriptive general frames as well as the discrete duality between complete atomic Boolean algebras and Kripke frames, and we use this framework to discuss canonicity theory. The second part is an introduction of correspondence theory in an algebraic way, which is modular and easy to generalize to other semantic settings.
Abstract:This is a theoretical development of epistemic logic to problems concerning the relationship between perception and knowledge. We closely follow the approach of Seligman, Liu and Girard’s “Logic in the Community” which proposes a two-dimensional multi-agent epistemic logic, in which the model operator K (knows) is supplemented with a ‘social’ operators which allow reasoning about relations between agents. The logic also uses operators from hybrid logic, such as nominals n, which name agents, the perspective shifting operator @n, which moves to agent n’s perspective, and the downarrow operator ↓x, which names the current agent a rigid name x. We propose an axiomatisation and completeness proof, using the step-by-step method, first for the basic logic and then for the case of downarrow, which is more involved. While the framework is very general, we are specifically interested in a perceptual agent-oriented operator S (sees). Axioms for the interaction of seeing and knowing are explored. We then consider dynamic extensions of the basic logic with public announcement and “observational” announcement, in which information is given only to agents who can see the announcer.
Abstract:
近代来在科学哲学中,因果性已取代定律成为显学。笔者试图论证:James Woodward 的不变性要求太弱,可能有自相矛盾或琐碎无聊的不变性;模态性要求太强,可能出现实际上不太合理的因果关系;定律中所包含的深层次概念,可能无法从因果图中导出;特殊科学实际上很难进行有效操控,数理传统可能比实验传统发挥更大的作用。笔者建议,科学定律与因果性可以有效互补,定律“大处着眼”,因果性“小处着手”。
关键词:定律,因果性,其它情况均同定律
Abstract:
Public opinion is a common yet complex phenomenon. We present a formal theory of public opinion for a rigorous platform for the topic, in which opinions are represented by logical formulas. The method of norm forms is used to simplify the problem. We present various aggregation conditions and aggregation functions. We study in detail a specific function. It reflects a common usage that public opinions are the most popular opinions among the public. We prove a characterization theorem for this kind of public opinions, saying that it is the only one that satisfies six fairness conditions.
Abstract:In the traditional so-called Tarski’s Truth Definition the semantics of first order logic is defined with respect to an assignment of values to the free variables. A richer family of semantic concepts can be modelled if semantics is defined with respect to a set (a “team”) of such assignments. This is called team semantics. Examples of semantic concepts available in team semantics but not in traditional Tarskian semantics are the concepts of dependence and independence. Dependence logic is an extension of first-order logic based on team semantics. It has emerged that teams appear naturally in several areas of sciences and humanities, which has made it possible to apply dependence logic and its variants to these areas. In my talk I will give a quick introduction to the basic ideas of team semantics and dependence logic as well as an overview of some new developments, such as quantitative analysis of team properties, a framework for a multiverse approach to set theory, and probabilistic independence logic inspired by the foundations of quantum mechanics.
Abstract:We study the identification and estimation of long-term treatment effects when both experimental and observational data are available. Since the long-term outcome is observed only after a long delay, it is not measured in the experimental data, but only recorded in the observational data. However, both types of data include observations of some short-term outcomes. In this paper, we uniquely tackle the challenge of persistent unmeasured confounders, i.e., some unmeasured confounders that can simultaneously affect the treatment, short-term outcomes and the long-term outcome, noting that they invalidate identification strategies in previous literature. To address this challenge, we exploit the sequential structure of multiple short-term outcomes, and develop three novel identification strategies for the average long-term treatment effect. We further propose three corresponding estimators and prove their asymptotic consistency and asymptotic normality. We finally apply our methods to estimate the effect of a job training program on long-term employment using semi-synthetic data. We numerically show that our proposals outperform existing methods that fail to handle persistent confounders.
Abstract:
Reasoning in social context has many important aspects, one of which is the reasoning about strategic abilities of individuals (agents) and groups (coalitions) of individuals to guarantee the achievement of their desired objectives while acting within the entire society. Several logical systems have been proposed for formalising and capturing such reasoning, starting with the Coalition Logic (CL), the Alternating Time Temporal Logic (ATL) and some extensions of these, introduced the early 2000s.
Coalition Logic provides a natural, but rather restricted perspective: the agents in the proponent coalition are viewed as acting in full cooperation with each other but in complete opposition to all agents outside of the coalition, which are thus treated as adversaries. The Alternating Time Temporal Logic extends Coalition Logic with temporal operators allowing for expressing long-term temporised goals.
The strategic interaction in real life is much more complex, usually involving various patterns combining cooperation and competition. To capture these, more expressive and versatile logical frameworks are needed.
In this talk I will first present briefly Coalition Logic and then will introduce and discuss some more expressive and versatile logical systems, including: (i) the Socially Friendly Coalition Logic (SFCL), enabling formal reasoning about strategic abilities of individuals and groups to ensure achievement of their private goals while allowing for cooperation with the entire society; (ii) the complementary, Group Protecting Coalition Logic (GPCL), capturing reasoning about strategic abilities of the entire society to cooperate in order to ensure achievement of the societal goals, while simultaneously protecting the abilities of individuals and groups within the society to achieve their individual and group goals.
Finally, time permitting, I will discuss briefly conditional strategic reasoning, where agents reason about their strategic abilities conditional on the actions that they expect the other agents to take.
In conclusion, I will take a more general perspective on a unifying logic-based framework for strategic reasoning in social context.
Abstract:
I present a topological epistemic logic, motivated by a famous epistemic puzzle: the Surprise Exam Paradox. It is a modal logic, with modalities for knowledge (modelled as the universal modality) and knowability of a proposition (represented by the topological interior operator), and (un)knowability of the actual world. The last notion has a non-self-referential reading (modelled by Cantor derivative: the set of limit points of a given set) and a self-referential one (modelled by Cantor’s perfect core of a given set: its largest subset without isolated points). I completely axiomatize this logic, showing that it is decidable and PSPACE-complete. I point its connections to my older joint work on topological mu-calculus, and finally I apply it to the analysis of the Surprise Exam Paradox (in both its non-self-referential and its self-referential versions). This talk is based on recent joint work with Nick Bezhanishvili and David Fernandez-Duque.
Reference.
Baltag, A.; Bezhanishvili, N.; and Fern´andez-Duque, D. 2022. The topology of surprise. Accepted for presentation at the KR workshop, affiliated with LICS 37. To appear in the KR Proceedings.
Baltag, A.; Bezhanishvili, N.; and Fern´andez-Duque, D. 2021. The topological mu-calculus: completeness and decidability. In Proceedings. of LICS 36, 1–13. IEEE Press.
Abstract:Classical philosophical analyses seek to explain knowledge as deriving from more basic notions. The influential “knowledge first” program in epistemology reverses this tradition, taking knowledge as its starting point. From the perspective of epistemic logic, however, this is not so much a reversal as it is the default—the field arguably begins with the specialization of “necessity” to “epistemic necessity”; that is, it begins with knowledge. In this context, putting knowledge second would be the reversal. This work motivates, develops, and explores such a “knowledge second” approach in epistemic logic, founded on distinguishing what a body of evidence actually entails from what it is (merely) believed to entail. We import a logical framework that captures exactly this distinction, use it to define formal notions of (internal and external) justification, and investigate applications to the KK principle, the regress problem, and the definition of knowledge.
Abstract:Carnap’s Problem, or Carnap’s Question, as Denis Bonnay and I understand it, is to what extent a consequence relation in some logical language fixes the meaning of the logical constants in that language. This can be seen as relevant to the issue of what ‘logical’ means. Also, it seems that people can have fairly robust intuitions about ‘what follows from what’ without having clear ideas about logicality, so it is of some interest to see if and how the former determines the latter. I will give an overview of what has been achieved in this area so far, concerning classical first-order logic, logics with generalized quantifiers, modal logic, and some partial results for intuitionistic propositional logic (the latter is joint work with Haotian Tong). I end by briefly discussing how this approach fares in comparison to other ideas about logicality.
Events in 2021-2022 Autumn Semester
Abstract: Using a special kind of Birkhoff lattices, we construct a permutation model in which there exists a finite-to-one function from the symmetric group of an infinite set A onto A, which cannot exist even in the presence of the axiom of countable choice. This is a joint work with Jiachen Yuan.
Abstract: 新一代人工智能以大数据和机器学习技术为核心,实行的是联结主义的路径。该路径在场景封闭的数据密集型应用中取得了巨大成功,但面临可解释性差、伦理对齐困难、认知推理能力弱等瓶颈问题。为了在一定程度上解决这些问题,不可避免地涉及到对开放、动态、真实环境中信息的刻画,以及对人类推理和解释机制的建模。形式论辩可以提供不一致情境下知识表示与推理的通用机制,与偏好、权重、概率等决策因素的灵活结合机制,局部化和模块化的语义高效计算机制,以及基于论证和对话的可解释机制等。有机结合形式论辩与现有大数据和机器学习技术,有望在一定程度上突破现有技术瓶颈,促进新一代人工智能的健康发展。
Abstract: Reasoning with generalized quantifiers in natural language combines logical and arithmetical features, transcending divides between qualitative and quantitative. This practice blends with inference patterns in ‘grassroots mathematics’ such as pigeon-hole principles. Our topic is this cooperation of logic and counting, studied with small systems and gradually moving upward. We start with monadic first-order logic with counting. We provide normal forms that allow for axiomatization, determine which arithmetical notions are definable, and conversely, discuss which logical notions and reasoning principles can be defined out of arithmetical ones. Next we study a series of strengthenings in the same style, including second-order versions, systems with multiple counting, and a new modal logic with counting. As a complement to our fragment approach, we also discuss another way of controlling complexity: changing the semantics of counting to reason about ‘mass’ or other aggregating notions than cardinalities. Finally, we return to natural language, confronting our formal systems with linguistic quantifier vocabulary, monotonicity reasoning, and procedural semantics via semantic automata. We conclude with some pointers to further entanglements of logic and counting in formal systems, in philosophy of logic, and in cognitive psychology.
Paper available at: https://eprints.illc.uva.nl/id/eprint/1813/1/Logic.Counting.pdf
Abstract: Much of causality and causal inference can be understood profitably through the lens of modern logic. In this talk we present two applications of this study to artificial intelligence. The first concerns the theoretical and empirical limitations of causal inference from observational and experimental data. The second involves the use of causal-logical tools to derive abstract and human-interpretable analyses of opaque AI systems trained with large, complex data. The broader aim of the talk will be to illustrate the potential for symbiosis between theoretical work in logic and practical work in AI.
Abstract: We discuss several questions regarding doxastic logic with propositional quantifiers. First, suppose we take the normal modal logic KD45 as the starting point of the logic of belief, with propositional quantifiers, what logics are available to us, and can we show completeness with respect to some established semantics for belief? To this end, we identify two key principles: the immodesty principle (I believe that everything I believe is true), and the quantificational introspection principle (if no matter what p is, I believe in phi, then I believe that no matter what p is, I believe in phi). We show that, on the one hand, to invalidate the immodesty principle, we need to deviate from the standard possible world semantics, and on the other hand, it is very hard to avoid the quantificational introspection principle since every complete modal algebra validating KD45 also validates it, though it is not derivable in KD45 with the usual axioms for propositional quantifiers. We will also touch on the issue of belief as credence 1. Then, time permitting, we shall consider deviations even from KD45. We will show how rejecting immodesty also puts pressure on introspection (in particular negative introspection) and discuss logical issues specifically with propositional quantifiers coming out of rejecting introspection.
Abstract: As concerns the explication of the intuitive notion of truthmaking, Barry Smith has an insight that deserves more attention. Basically, in his view, an object x makes a proposition
true iff (α) x necessitates
and (β)
is representationally closely tied with x. To be more specific, he suggests that (β) is fulfilled only if x is among
’s ontological commitments. I appreciate his basic insight but reject his specific suggestion. I argue that we can make a more attractive proposal from his basic insight if we take into consideration that the close tie can also be realized by
’s being about x.
Abstract: Justification logics are closely related to modal logics and can be viewed as a refinement of the latter with machinery for justification manipulation. Justifications are represented directly in the language by terms, which can be interpreted as formal proofs in a deductive system, evidence for knowledge, and so on. This more expressive language proved beneficial in both proof theory and epistemology and helped investigate problems ranging from a classical provability semantics for intuitionistic logic to the logical omniscience problem.
In this talk, we will give an introduction to justification logic and present recent developments in the field such as subset models, conflict tolerant logics, and formalizations of zero-knowledge proofs.
Abstract: I will consider different alternatives for giving logic models of ability. First I will explain the difference between possibilities for action and (general) abilities. Then I will focus on the role of knowledge and knowing how in understanding and modelling ability. The importance of modeling these concepts is motivated by discussing their application in symbolic and responsible AI.
Abstract: Nonstandard analysis, a powerful machinery derived from mathematical logic, has had many applications in various areas of mathematics such as probability theory, stochastic processes, mathematical physics, functional analysis, and mathematical economics. Nonstandard analysis allows construction of a single object a hyperfinite probability space which satisfies all the first-order logical properties of a finite probability space, but which can be simultaneously viewed as a measure-theoretical probability space via the Loeb construction. As a consequence, the hyperfinite/measure duality has proven to be particularly in porting discrete results into their continuous settings. We present several applications of this novel approach:
(1) Extending known results for discrete Markov processes to analogues results for general Markov processes (e.g., ergodicity of Markov processes, mixing and hitting times of Markov processes);
(2) Establishing tight connections between frequentist optimality and Bayes optimality for general statistical decision problems;
(3) Existence of Walrasian equilibrium for exchange/production economy models
that are specific to climate change.
Abstract: Dynamic Epistemic Logic can be used for Epistemic Planning, as shown in several recent works, ranging from theoretical proposals to actual implementations on robots. A crucial part of automated epistemic planning is to compute perspective shifts that let agents take into account the knowledge of others. So far, these perspective shifts are usually done using explicit Kripke models which may grow exponentially in the number of agents or propositions. I will discuss methods to tackle this state-explosion problem and show how to compute perspective shifts without explicit Kripke models. The two methods I will present are based on symbolic structures and succinct models. Both are compact representations from previous literature showing how to speed up model checking DEL. The new definitions aim to make epistemic planning more efficient in the future. Most of the talk will be based on the article available here: (https://malv.in/2020/EpiP-perspective-shifts.pdf) Time permitting, I will also present related software recently developed by my students and myself.
Abstract:传统分析认为“都”表示“总括”(吕叔湘,1980)。我们发现[复数性名词成分+“都”]中“都”是否出现受语境制约。大致说来,当复数性名词成分所在的句子没有独立完整回答语境中的问题时,“都”最好不出现;反之,“都”通常需要出现。从“都”的这一语境适用条件出发,我们提出“都”总括的是语境中的话题/问题(Roberts 1996);“总括”说的是,“都”表达了与之结合的句子包括了当前话题下的所有内容,因而具有“排除谈话中其他人或事物”(陆庆和,2006)的功能。同时,为了满足“总括”,跟“都”结合的句子必须取分配解读,这造成了“都”的“分配效应”。我们认为,这种解释可以让我们对“都”的“总括义”,“甚至义”和“反预期”效果有统一的认识。更进一步,我们提出“都”的“总括义”是一个预设,这使我们可以通过“强制性预设”现象来解释“都”为什么在某些环境下必须出现(Liu 2021)。最后,本次报告将探讨如何将我们的分析推广至“都”与其他名词成分搭配的情况,以及解释“都,就”为何经常出现在无条件句与条件句的后件中。
Abstract: For a long time now, deontic logicians have studied the typology of legal rights that Wesley Hohfeld proposed at the beginning of the 20th century. This has become known as the theory of normative positions. However, one prominent type of legal rights, so-called epistemic rights, has not yet been systematically studied in the hohfeldian typology. In this talk, I will present recent and ongoing work with Réka Markovich (Luxembourg) in which we take the first steps towards filling this gap. I will consider two prominent epistemic rights, the right to know and freedom of thought, and one application of the resulting theory to a recent example in US law.
Abstract: 集体认定是按一定的规则,综合集体中每个人的意见,对命题的一种断定。法律审判中的陪审员制度,社会政治生活中的选举、决议等都是集体认定的典型例子。
人们很早就发现,集体认定中会出现不一致,合理的认定得到的若干命题放在一起可以是不一致的。人们的研究往往从社会学的角度出发,集中在对于规则合理性的讨论,而不是对不一致现象本身的讨论。
集体认定还有一种类似于不一致的现象:合取原则的失效。而在大多数关于集体认定的研究中,合取原则失效的问题并没有得到充分讨论。
本文从现有的集体认定的规则出发,总结出一些基本的原则,包括认定集体中的个人的原则和认定集体的集体的原则,在这些原则的基础上建立了集体认定逻辑系统,在此逻辑系统中严格定义了不一致和合取原则,给出并证明了不一致现象产生和合取原则失效的条件。
Events in 2020-2021 Spring Semester
- 2021-5-20 Lian Zhou: Co-reference Without Referent
2021-5-13 Qingbian Ma: Decision Making in the Emergency Room
2021-4-29 Qi Feng: Cantor and Set Theory
2021-4-22 Jialong Zhang: Bertrand Russell and Mathematical Logic
Events in 2020-2021 Autumn Semester
- 2021-1-10, Lingyuan Ye: Uniformity, Contingency, and Self-reference in Arithmetic & Xiao Li: Towards a Semantic Concept of Aboutness
- 2020-12-25, Duoyi Fei: A Defense for the State of Internal Knowledge
- 2020-12-04, Changsheng Lai: Epistemic Gradualism and the Gradability of Truth
- 2020-12-11, Kang Liu: From Vectors to Symbols.
- 2020-11-12, Thomas Bolander and Lasse Dissing: Implementing Theory of Mind on a Robot Using Dynamic Epistemic Logic.
- 2020-11-06, Zhisheng Huang: Application of Logic in Data Mining
Events in 2019-2020 Autumn Semester
- 2020-1-08, Fengkui Ju: Towards a Logical Theory of Temporal Conditionals & Xinwen Liu: Jin Yuelin’s Encounter with C.P. Peirce
- 2019-11-28, Shengyang Zhong: On Quantum Logic
- 2019-11-14, Martin Stokhof: Natural Language, Formal Language: a Complex Relationship
- 2019-10-23, Dazhu Li: Dynamic Epistemic Logic of Social Influence; Kaibo Xie (UvA and Tsinghua) : Formal Semantics for Counterfactuals
- 2019-10-10, Frank Veltman: On Imperatives in Natural Language.