2019年联合国教科文组织确立每年的1月14日为世界逻辑日（The World Logic Day），旨在使逻辑学的历史、逻辑概念的重要性和逻辑学的实践意义能够得到跨学科科学界和公众的关注。无论在什么文化背景下，思维、推理与认知的规律是人类亘古不变的追求，也构成了逻辑学的篇章。逻辑学的历史是世世代代逻辑学者们共同谱写的：提出一个新概念，给出一个新语义，证明一个新定理，这些都是我们的生活日常。在2025年世界逻辑日到来之际，我们分享逻辑学研究中心过去一年的部分教学科研成果，与同仁们一起庆祝。衷心祝愿大家在研究上灵感迸发，思如泉涌！世界逻辑日快乐！
刘奋荣、司马亭（Martin Stokhof）著： Logic, Language and Philosophy: An Introduction to Standard Logic
Peter Pagin、魏达格（Dag Westerståhl）主编：Theoria: Volume 90, Issue 5: Special Issue: Rolf Schock Prize in Logic and Philosophy 2022
同时，中心师生的英文论文发表在 Journal of Philosophical Logic、Journal of Logic and Computation、Studia Logica 等知名国际期刊和 AiML、DaLí 、TACL 等知名国际会议的论文集。
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刘奋荣、司马亭著
Logic, Language and Philosophy
Logic, Language and Philosophy:An Introduction to Standard Logic 刘奋荣、司马亭著由斯坦福大学语言与信息研究中心出版社（CSLI Publications）出版 内容简介 本书凝聚了两位教授在清华多年教学的精华，不仅系统介绍了逻辑学的核心概念与技术（涵盖命题逻辑和谓词逻辑），还深入探讨了这些概念和技术引发的哲学问题。此外，扩展部分还涉及多值逻辑、内涵逻辑和语用学等内容。据作者们在《序》中所述，本书的写作动机主要源于学生的需求。在清华，参加该课程的学生背景十分多样，既有理工科的学生，也有哲学、人文与社会科学的学生，还有来自计算机科学、数学和人工智能领域的学生。因此，希望该书的出版能为不同背景的读者提供学习逻辑学的机会。该书的中文版本已准备完毕，预计将于2025年由人民邮电出版社出版。
清华大学-阿姆斯特丹大学联合培养博士项目学生陈谦、清华大学哲学系副教授石辰威与山西大学哲学学院副教授王奕岩合作的文章 Reasoning about Dependence, Preference and Coalitional Power 在英文期刊 Journal of Philosophical Logic 上发表。
Abstract: This paper presents a logic of preference and functional dependence (LPFD) and its hybrid extension (HLPFD), both of whose sound and strongly complete axiomatization are provided. The decidability of LPFD is also proved. The application of LPFD and HLPFD to modelling cooperative games in strategic form is explored. The resulted framework provides a unified view on Nash equilibrium, Pareto optimality and the core. The philosophical relevance of these game-theoretical notions to discussions of collective agency is made explicit. Some key connections with other logics are also revealed, for example, the coalition logic, the logic of functional dependence and the logic of ceteris paribus preference.
Journal of Logic and Computation
清华大学金岳霖讲席教授范丙申（Johan van Benthem）与阿姆斯特丹大学逻辑、语言和计算研究院副教授Nick Bezhanishvili合作的文章 Modal structures in groups and vector spaces 在英文期刊 Journal of Logic and Computation 上发表。
Abstract: Vector spaces contain a number of general structures that invite analysis in modal languages. The resulting logical systems provide an interesting counterpart to the much better-studied modal logics of topological spaces. In this programmatic paper, we investigate issues of definability and axiomatization using standard techniques for modal and hybrid languages. The analysis proceeds in stages. We first present a modal analysis of commutative groups that establishes our main techniques, next we introduce a new modal logic of linear dependence and independence in vector spaces and, finally, we study a modal logic for describing full-fledged vector spaces. While still far from covering every basic aspect of linear algebra, our discussion identifies several leads for more systematic research. 浙江大学哲学学院教授廖备水、清华大学哲学系教授刘奋荣、卢森堡大学计算机科学学院教授Leendert van der Torre以及中国科学技术大学信息科学技术学院电子工程与信息科学系教授周熠合作的文章 Advancing Logic in AI: insights from the LNGAI 2021 Workshop 在英文期刊 Journal of Logic and Computation 上发表。
Studia Logica
清华大学-阿姆斯特丹大学联合培养博士项目学生陈谦与中山大学哲学系教授马明辉合作的文章 The McKinsey Axiom on Weakly TransitiveFrames 在英文期刊 Studia Logica上发表。
Abstract: The McKinsey axiom has a local first-order correspondent on the class of all weakly transitive frames . It globally corresponds to Lemmon’s condition on . The formula is canonical over the weakly transitive modal logic . The modal logic has the finite model property. The modal logics () form an infinite descending chain in the interval and each of them has the finite model property. Thus all the modal logics and () are decidable. 清华大学哲学系刘奋荣教授和中国科学院哲学研究所、中国科学院大学人文学院李大柱副教授，日本北海道大学文学研究院哲学伦理学研究室佐野胜彦教授合作的文章 Hybrid Logic of the Hide and Seek Game 在英文期刊 Studia Logica 上发表。
Abstract: The logic of the hide and seek gamewas proposed to capture interactions between agents in pursuit-evasion environments. In this paper, we explore a hybrid extension ofand show that such an extension is beneficial in several aspects. We will show that it improves the technical properties of the resulting logical system, and expands the potential applications of the system. Specifically, we will investigate the expressive power of the hybrid logic of the hide and seek gameand its crucial fragment, at both model and frame levels. We will present complete Hilbert-style proof systems for both the logicsand, which in fact provides a solution to a known open problem.
Abstract: In this paper, we propose Point-set Neighborhood Logic (PSNL) to reason about neighborhood structures. The bimodal language of PSNL is defined via a mutual induction of point-formulas and set-formulas. We show that this simple language is equally expressive as the language of Instantial Neighborhood Logic (INL). As the main results, we first give two complete proof systems, one in Hilbert-style and one in Gentzen sequent-style, each featuring two intertwined K-like systems. The proof of strong completeness of the Hilbert-style system is based on a direct canonical model construction without relying on a normal form. Based on the sequent calculus, we establish constructively the uniform interpolation property of PSNL, from which that of INL follows.
DaLí
国际会议 DaLí 的论文集于2024年正式出版，其中包含清华大学逻辑学研究中心师生的三篇英文论文。会议全名为：DaLí: Dynamic Logic – New trends and applications，于2023年9月15-16日在格鲁吉亚第比利斯举行。DaLí 2023 研讨会的目的是将对行动的形式化研究有共同兴趣的研究人员（从学术界到工业界等，从数学到计算机科学等）聚集在一起，展示他们的工作，促进讨论并鼓励合作。
题目：Axiomatization of Hybrid Logic of Link Variations (边变换混合逻辑的公理化)作者：杜鹏昊（清华哲学系），陈谦（清华哲学系）摘要：In this paper, 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. For the global level, the logic of global link variations based on hybrid logic is introduced, which involves global link cutting, adding and rotating simultaneously. A Hilbert-style calculus is provided. By constructing a family of canonical models inductively, we prove that is strongly complete with respect to . For the local level, we extended the logic of link deletion introduced in [Li, 2020] to , which is based on the hybrid logic and contains local dynamic operators for definable link cutting, adding and rotating. By defining named local dynamic operators and providing recursion axioms for them, we introduce a sound and strongly complete calculus for . Moreover, we show that for an arbitrarily set of global/local dynamic operators, the calculus / is still sound and strongly complete w.r.t the logic /.题目：Logic of the Hide and Seek Game: Characterization, Axiomatization, Decidability (捉迷藏博弈的逻辑：刻画、公理化及可判定性)作者：陈谦（清华哲学系），李大柱（中科院哲学所）摘要：The logic of the hide and seek game LHS was proposed to reason about search missions and interactions between agents in pursuit-evasion environments. As proved in literature, having an equality constant in the language of LHS drastically increases its computational complexity: the satisfiability problem for LHS with multiple relations is undecidable. In this work, we improve the existing result by showing that LHS with a single relation is undecidable. With the findings of existing literature, we provide a van Benthem style characterization theorem for the expressive power of the logic. Finally, by ‘splitting’ the language of LHS−, a crucial fragment of LHS without the equality constant, into two ‘isolated parts’, we provide a complete Hilbert style proof system for LHS− and prove that its satisfiability problem is decidable, whose proofs would indicate significant differences between the proposals of LHS− and of ordinary product logics. Although LHS and LHS− are frameworks for interactions of 2 agents, all results in the article can be easily transferred to their generalizations for settings with any n > 2 agents.题目：A Logical Approach to Doxastic Causal Reasoning (信念因果推理的逻辑进路)作者：谢凯博（武汉大学哲学系），何清瑜（清华哲学系），刘奋荣（清华哲学系）摘要：Belief revision and causality play an important role in many applications, typically, in the study of database update mechanisms and data dependence. New contributions on causal reasoning are continuously added to the pioneering works by Pearl, Halpern and others. Though there is a long tradition of modeling belief revision in philosophical logic, the entanglement between belief revision and causal reasoning has not yet been fully studied from a logical view. In this paper, we propose a new formal logic for doxastic causal reasoning. With examples, we illustrate that our framework explains the rational way of belief revision based on causal reasoning. We further study the general properties of the logic. A complete axiomatization, as well as a decidability result, will be given. In addition, we believe our work will shed light on understanding the relation between qualitative and quantitative approaches toward (causal) dependence in general.
TACL
清华大学-阿姆斯特丹大学联合培养博士项目学生陈谦的论文摘要 Pretabular Tense Logics over 在国际会议 Topology, Algebra, and Categories in Logic (TACL 2024) 的摘要集中发表。 简介: In this work, we study the pretabular tense logics over . For each logic , let Pre() denote the set of pretabular logics extending . We show that |Pre()|=5 and |Pre()|=|Pre()|=12. Moreover, we prove that there are countably many pretabular tense logic extending , which is the tense logic of 'zigzags' with clusters.
LNGAI
清华大学哲学系教授刘奋荣、博士生王威、博士生杨思思合作的文章 Towards a Logical Approach to Recommendations 在国际会议 Logics for New-Generation AI (LNGAI 2024) 的论文集上发表。
Abstract: In the digital era, users encounter an endless stream of recommendations. The development of recommendation systems in AI has attracted extensive attention, yielding a substantial body of literature. However, we have not encountered any logical systems for reasoning about recommendation systems, despite the immense amount of reasoning involved in making recommendations. In this paper, 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 has the tree model property and that its model-checking problem can be solved in polynomial time, for which we propose an algorithm and prove its correctness. We believe that our work has the potential to advance personalized recommendations.
