This paper analyzes legal fact-argumentation in the framework of the argumentation-based litigation game by Xiong :16–19, 2012). Rather than as an ontological one, an ALG treats a legal fact as a fact-qua-claim whose acceptability depends on the reasons supporting it. In constructing their facts-qua-claims, parties to an ALG must interact to maintain a game-theoretic equilibrium. We compare the general interactional constraints that the civil and common law systems assign, and detail what the civil, administrative, and criminal codes of mainland (...) China require of the suitor, the respondent, and the trier to establish their respective S-, R- and T-facts. We also offer an improved version of the legal syllogism. (shrink)

Becker argued Confucianism lacked of argumentation, dialogue and debate. However, Becker is wrong. First, the purpose of philosophical argumentation is to justify an arguer’s philosophical standpoints. Second, both Confucius’ Analects and Mencius’ Mencius were written in forms of dialogues. Third, the content of each book is the recorded utterance and the purpose of dialogue is to persuade its audience. Finally, after Confucius, Confucians’ works have either argued for those unjustified standpoints or re-argued about some justified viewpoints in the Analects.

Mencius, the second sage of Confucianism after Confucius, is well known for his subtle argumentative skills. Mencius did not develop his own argumentation theory, but argumentation practices, including his political argumentation, have enormously inspired later scholars in China to develop argumentation theories. In this paper, we try to reconstruct Mencius’s political argumentation from perspectives of both strategic maneuvering developed by van Eemeren et al. in argumentation theory and truth-functional logic in formal logic. The aim is to manifest the Dao, a (...) rational balance among logical, dialectical and rhetorical dimensions in Mencius’s political argumentation. The results indicate that Mencius’s political argumentation is not only logically justified but also shown to have maneuvered strategically between reasonableness and effectiveness, and that human beings have a common ground of formal and substantial logos, which makes it possible for people from different cultural groups to communicate rationally. (shrink)

In a recent paper, “One Logician’s Perspective on Argumentation”, van Benthem expressed his reservations on Toulmin’s diagnosis and abandonment of formal logic, and argued that Toulmin was wrong for leading the study of argumentation apart from formal approach. In this paper we will try to reveal two se-rious misunderstandings of Toulmin’s ideas in his discussions, and thereby make an apology for Toulmin.

This comprehensive volume features the proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, held in Hangzhou, China on September 8-9 and 11-12, 2023. The collection offers a diverse range of papers that explore the intersection of logic, artificial intelligence, and law. With contributions from some of the leading experts in the field, this volume provides insights into the latest research and developments in the applications of logic in (...) these areas. It is an essential resource for researchers, practitioners, and students interested in the latest advancements in logic and its applications to artificial intelligence and law. (shrink)

"Yang Xiong is the most useless of all. He was truly a rotten Confucian."Zhu Xi (11301200 A.D.)With this comment from Song Dynasty Neo-Confucian Zhu Xi, the work of Han Dynasty philosopher Yang Xiong (53 B.C.18 A.D.) was effectively relegated to the dustbin of Chinese intellectual history. While influential in the Later Han as the clearest expression of the Old Text Confucian school, Yang's Fa yan has received little attention from Western scholars and appears here in a rare annotated (...) English translation.Written during the transition between the Former and Later Han Dynasties, the Fa yan is a notoriously elusive text that was stylistically modeled on the Analects of Confucius. Denigrated by later Neo-Confucians for his association with Han usurper Wang Mang, Yang Xiong served both the Former Han and Xin imperial courts as a court poet and scholar, and was well known for being a reclusive personality, earning him a reputation as a "hermit at court." Most famous for his position that human nature is a mixture of good and evil, Yang Xiong's philosophy stands in clear contrast to the syncretic Confucianism of his day as a reformer's vision of proper self-cultivation and statecraft.This volume presents an annotated translation of the entire text, focusing on the passages that elucidate Yang's discussion of the core concepts of the Confucian school. The translator's commentary traces the text's major philosophical concepts to their roots in Warring States era philosophy, noting stylistic and conceptual allusions to the Analects and Mencius, among other texts. Also included are a discussion of Yang's biography and the influence of the eremitic ideal on his life and thought. (shrink)

Intuitionistic propositional logic with Galois negations ( \(\mathsf {IGN}\) ) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair \((\lnot,{\sim })\) and dual Galois pair \((\dot{\lnot },\dot{\sim })\) of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for \(\mathsf {IGN}\) are developed. A Hilbert-style axiomatic system \(\mathsf {HN}\) is given for \(\mathsf {IGN}\), and Galois negation logics are defined as extensions of \(\mathsf {IGN}\). We give the bi-tense (...) logic \(\mathsf {S4N}_t\) which is obtained from the minimal tense extension of the modal logic \(\mathsf {S4}\) by adding tense operators. We give a new extended Gödel translation \(\tau \) and prove that \(\mathsf {IGN}\) is embedded into \(\mathsf {S4N}_t\) by \(\tau \). Moreover, every Kripke-complete Galois negation logic _L_ is embedded into its tense companion \(\tau (L)\). (shrink)

This article investigates Charles Peirce’s development of logical calculi for classical propositional logic in 1880–1896. Peirce’s 1880 work on the algebra of logic resulted in a successful calculus for Boolean algebra. This calculus, denoted byPC, is here presented as a sequent calculus and not as a natural deduction system. It is shown that Peirce’s aim was to presentPCas a sequent calculus. The law of distributivity, which Peirce states in 1880, is proved using Peirce’s Rule, which is a residuation, inPC. The (...) transitional systems of the algebra of the copula that Peirce develops since 1880 paved the way to the 1896 graphical system of the alpha graphs. It is shown how the rules of the alpha system reinterpret Boolean algebras, answering Peirce’s statement that logical graphs supply a new system of fundamental assumptions to logical algebra. A proof-theoretic analysis is given for the connection betweenPCand the alpha system. (shrink)

A finitely alternative normal tense logic \ 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 \\) is described. There are \ logics in \\) without the finite model property, and only one pretabular logic in \\). There are \ logics in \\) which are not finitely axiomatizable. For \, there are \ logics in \\) without the FMP, and infinitely many pretabular (...) extensions of \. (shrink)

Every Berman’s variety \ which is the subvariety of Ockham algebras defined by the equation \ and \) determines a finitary substitution invariant consequence relation \. A sequent system \ is introduced as an axiomatization of the consequence relation \. The system \ is characterized by a single finite frame \ under the frame semantics given for the formal language. By the duality between frames and algebras, \ can be viewed as a \-valued logic as it is characterized by a (...) distributive lattice of \ elements with a unary operator. Moreover, a structural-rule-free, cut-free and terminating sequent system \ is established for \. The Craig interpolation property of \ is shown proof-theoretically utilizing \. (shrink)

A deterministic weakening \ of the Belnap–Dunn four-valued logic \ is introduced to formalize the acceptance and rejection of a proposition at a state in a linearly ordered informational frame with persistent valuations. The logic \ is formalized as a sequent calculus. The completeness and decidability of \ with respect to relational semantics are shown in terms of normal forms. From an algebraic perspective, the class of all algebras for \ is described, and found to be a subvariety of Berman’s (...) variety \. Every linearly ordered frame is logically equivalent to its dual algebra. It is proved that \ is the logic of a nine-element distributive lattice with a negation. Moreover, \ is embedded into \ by Glivenko’s double-negation translation. (shrink)

Charles Peirce’s alpha system \ is reformulated into a deep inference system where the rules are given in terms of deep graphical structures and each rule has its symmetrical rule in the system. The proof analysis of \ is given in terms of two embedding theorems: the system \ and Brünnler’s deep inference system for classical propositional logic can be embedded into each other; and the system \ and Gentzen sequent calculus \ can be embedded into each other.

Hegel’s theory of indexicality appears in the first chapter of the Phenomenology of Spirit, Sensuous-Certainty (SC). Current interpretations of the meaning of the universals that Hegel attributes to indexicals diverge from one another. Such interpretations can be divided into three groups: the universals as Fregean senses, as properties expressed by predicates in complex demonstratives, and as contrastive and recollective repeatability. I argue that all three exegeses face difficulties. Fregean senses, as referent-dependent modes of presentation, are particulars rather than universals. The (...) interpretation that appeals to predicates in complex demonstratives confuses referential indeterminacy with context sensitivity. The view of universals as contrastive and recollective repeatability misses the point of Hegel’s relevant arguments regarding universals. I propose to understand the universal in question as an indexical expression type akin to David Kaplan’s character (linguistic rules for expression use). In SC, Hegel argues for an expression/reference distinction by appealing to the context sensitivity of indexicals. (shrink)

The study aims to explore the roles of Massive Open Online Courses based on deep learning in college students’ English grammar teaching. The data are collected using a survey. After the experimental data are analyzed, it is found that students have a low sense of happiness and satisfaction and are unwilling to practice oral English and learn language points in English learning. They think that college English learning only meets the needs of CET-4 and CET-6 and does not take it (...) as the ultimate learning goal. After the necessity and problems in English grammar teaching are discussed, the advantages of flipped classrooms of MOOCs are discussed in English grammar teaching. A teaching platform is constructed to study the foreign language teaching mode under MOOCs, and classroom teaching is combined with the advantages of MOOCs following the principle of “teaching students according to their personalities” to improve the listening, speaking, reading, writing, and translation skills of foreign language majors. The results show that high-quality online teaching resources and the deep learning-based teaching environment can provide a variety of interactive tools, by which students can communicate with their peers and teachers online. Sharing open online communication, classroom discussion, and situational simulation can enhance teachers’ deep learning ability, like the ability to communication and transfer thoughts. Constructivism with interaction as the core can help students grasp new knowledge easily. Extensive communication and interaction are important ways for learning and thinking. The new model provides students with profound learning experience, expands the teaching resources of MOOCs around the world, and maximizes the interaction between online and offline teachers and students, making knowledge widely rooted in the campus and realizing the combination of online resources and campus classroom teaching. Students can learn the knowledge through autonomous learning and discussion before class, which greatly broadens the learning time and space. In the classroom and after class, the internalization and sublimation of knowledge are completed through group cooperation, inquiry learning, scenario simulation, display, and evaluation, promoting students to know about new knowledge and highlighting the dominant position of students. (shrink)

Graded epistemic logic is a logic for reasoning about uncertainties. Graded epistemic logic is interpreted on graded models. These models are generalizations of Kripke models. We obtain completeness of some graded epistemic logics. We further develop dynamic extensions of graded epistemic logics, along the framework of dynamic epistemic logic. We give an extension with public announcements, i.e., public events, and an extension with graded event models, a generalization also including nonpublic events. We present complete axiomatizations for both logics.

We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics we establish the completeness of fifteen modal logics of gamma graphs. We show that, besides logical necessity and possibility, Peirce proposed an epistemic interpretation of the (...) broken-cut modality, and that he was led to analyze constructions of knowledge in the style of epistemic logic. (shrink)

本書屬於比較哲學的工作，它涉及德國、中國與韓國的倫理學思考。第一、二章首先藉由梳理康德早期倫理學經由席勒倫理學到現象學倫理學的發展過程及其內在理路。此一發展涉及倫理學的基本問題：我們對於道德價值的「領 會」（Erfassung）究竟是什麼性質？此一問題具有跨文化的普遍意義，因此上述的思考為我們之探討中、韓儒學中的相關問題提供了極有用的參考架構。在中國儒學的發展當中，本書選擇了南宋朱熹與湖湘學派關於「 仁」的辯論（第三章），以及晚明劉宗周對於孟子的「四端」與《中庸》的「喜怒哀樂」之獨特詮釋（第四、五章）為探討個案。在韓國儒學的發展當中，本書則選擇了朝鮮儒者李退溪與奇高峰、李栗谷與成牛溪關於「四端」與 「七情」的辯論（第六、七、八章）為探討個案。在這三個個案中，朱子學作為共同的參照系統，與康德後期的倫理學有類似之處，即均預設理性與情感（或性與情）二分的主體性架構。反之，張栻等湖湘學者、劉蕺山、李退溪 與成牛溪將孟子的「四端」或《中庸》的「喜怒哀樂」視為與「七情」異質的形上之情，此點與現象學倫理學的基本方向不謀而合.

Peirce wrote in late 1901 a text on formal logic using a special Dragon-Head and Dragon-Tail notation in order to express the relation of logical consequence and its properties. These texts have not been referred to in the literature before. We provide a complete reconstruction and transcription of these previously unpublished sets of manuscript sheets and analyse their main content. In the reconstructed text, Peirce is seen to outline both a general theory of deduction and a general theory of consequence (...) relation. The two are the cornerstones of modern logic and have played a crucial role in its development. From the wider perspective, Peirce is led to these theories by three important generalizations: propositions to all signs, truth to scriptibility, and derivation to transformability. We provide an exposition of such proposed semiotic foundation for logical constants and point out a couple of further innovations in this rare text, including the sheet of assertion, correction as a dual of deduction and the nature of conditionals as variably strict conditionals. (shrink)

◎ 第一部全面探討東亞康德哲學的專著。 ◎ 完整呈現康德哲學傳東亞的過程，以及各國康德研究的意義與課題。 ◎ 本書由臺、中、日、韓學者共同合作，並以中、日、韓文出版，為東亞學術交流史上一大成就。 在西方哲學的發展當中，十八世紀的德國哲學家康德無疑是最受矚目的一位，他集西方傳統哲學之大成，也是現代西方哲學的共同源頭，具有承先啟後之關鍵地位。康德哲學於十九世紀中葉逐步傳入中國與日本、二十世紀初傳入 韓國，迄今已超過一百多年，對現代東亞文化具有難以估計的影響。 本書是第一部全面探討東亞學界如何接受與吸收康德哲學的專門論著，書中從接受史的角度闡述康德哲學傳入臺灣、中國、日本與韓國的過程；並從跨文化的視野，深入分析在此過程中涉及的哲學問題。誠如前輩康德專家鄭昕所 言：「超過康德，可能有新哲學，掠過康德，只能有壞哲學。」東亞各國對康德哲學的受容，並非只是被動吸收，而是反應各國學界所面臨的不同課題，呈現出多元化的樣貌。.

The Dutch Book Argument shows that an agent will lose surely in a gamble (a Dutch Book is made) if his degrees of belief do not satisfy the laws of the probability. Yet a question arises here: What does the Dutch Book imply? This paper firstly argues that there exists a utility function following Ramsey’s axioms. And then, it explicates the properties of the utility function and degree of belief respectively. The properties show that coherence in partial beliefs for Subjective (...) Bayesianism means that the degree of belief, representing a belief ordering, satisfies the laws of probability, and that coherence in preferences means that the preferences are represented by expected utilities. A coherent belief ordering and a utility scale induce a coherent preference ordering; a coherent preference ordering induces a coherent belief ordering which can be uniquely represented by a degree-of-belief function. The preferences (values) and beliefs are both incoherent or disordered if a Dutch Book is made. (shrink)

Editor’s AbstractTaiwanese Confucian Li Minghui is the best-known contemporary voice of New Confucianism. This is a published, edited transcript of an oral interview, so the style is somewhat informal, lively, even emotional. The first part of the interview primarily concerns the continued relevance of Confucianism in Taiwan, while the second focuses in part on Li's views of “Mainland New Confucianism.”.

A contraction-free and cut-free sequent calculus \ for semi-De Morgan algebras, and a structural-rule-free and single-succedent sequent calculus \ for De Morgan algebras are developed. The cut rule is admissible in both sequent calculi. Both calculi enjoy the decidability and Craig interpolation. The sequent calculi are applied to prove some embedding theorems: \ is embedded into \ via Gödel–Gentzen translation. \ is embedded into a sequent calculus for classical propositional logic. \ is embedded into the sequent calculus \ for intuitionistic (...) propositional logic. (shrink)

Peirce introduced Existential Graphs in late 1896, and they were systematically investigated in his 1903 Lowell Lectures. Alpha graphs for classical propositional logic constitute the first part of EGs. The second and the third parts are the beta graphs for first-order logic and the gamma graphs for modal and higher-order logics, among others. As a logical syntax, EGs are two-dimensional graphs, or diagrams, in contrast to the linear algebraic notations. Peirce's theory of EGs is not only a theory of logical (...) syntax but also a proof theory for many logics. A set of transformation rules of graphs defines a proof system for a graphical logic. In this... (shrink)

Modal logics for reasoning about social networks is currently an active field of research. There is still a gap, however, between the state of the art in logical formalisations of concepts related to social networks and the much more mature field of social network analysis. In this paper we take a step to bridge that gap. One of the key foundations of social network analysis is balance theory, which is used to analyse signed social networks where agents can have positive (...) or negative relationships. Certain combinations of positive and negative relationships are considered to be unbalanced, or unstable—in particular the occurrence of cycles with an odd number of negative relationships. Especially relatively short cycles with an odd number of negative relationships are thought to put pressure on the agents to change one or more of the involved relationships from negative to positive or the other way around. Most existing logics for reasoning about social networks are defined for unsigned networks. In this paper we develop a modal logic for reasoning about structural properties of signed social networks, and give a sound and complete Hilbert-style axiomatic system. Furthermore, we completely axiomatise classes of signed social networks that are balanced to a certain degree n, in the sense that there are no cycles of length up to n with an odd number of negative relationships. Finally, we completely axiomatise the class of all fully balanced complete signed social networks, i.e., networks where everyone is connected with everyone else. Axiomatic completeness is non-trivial because neither the balance properties, nor the dichotomy between positive and negative relations, are modally definable. The paper thus provides a logical basis for reasoning about signed social networks in general and balanced networks in particular. (shrink)

We present a dynamic approach to Peirce’s original construal of abductive logic as a logic of conjecture making, and provide a new decidable, contraction-free and cut-free proof system for the dynamic logic of abductive inferences with neighborhood semantics. Our formulation of the dynamic logic of abduction follows the philosophical and scientific track that led Peirce to his late, post-1903 characterization of abductive conclusions as investigands, namely invitations to investigate propositions conjectured at the level of pre-beliefs.

The finite model property (FMP) in weakly transitive tense logics is explored. Let \(\mathbb {S}=[\textsf{wK}_t\textsf{4}, \textsf{K}_t\textsf{4}]\) be the interval of tense logics between \(\textsf{wK}_t\textsf{4}\) and \(\textsf{K}_t\textsf{4}\). We introduce the modal formula \(\textrm{t}_0^n\) for each \(n\ge 1\). Within the class of all weakly transitive frames, \(\textrm{t}_0^n\) defines the class of all frames in which every cluster has at most _n_ irreflexive points. For each \(n\ge 1\), we define the interval \(\mathbb {S}_n=[\textsf{wK}_t\textsf{4T}_0^{n+1}, \textsf{wK}_t\textsf{4T}_0^{n}]\) which is a subset of \(\mathbb {S}\). There are (...) \(2^{\aleph _0}\) logics in \(\mathbb {S}_n\) lacking the FMP, and there are \(2^{\aleph _0}\) logics in \(\mathbb {S}_n\) having the FMP. Then we explore the FMP in finitely alternative tense logics \(L_{n,m}=L\oplus \{\textrm{Alt}_n^F, \textrm{Alt}_m^P\}\) with \(n,m\ge 0\) and \(L\in \mathbb {S}\). For all \(k\ge 0\) and \(n,m\ge 1\), we define intervals \(\mathbb {F}^k_{n,m}\), \(\mathbb {P}^k_{n,m}\) and \(\mathbb {S}^k_{n,m}\) of tense logics. The number of logics lacking the FMP in them is either 0 or \(2^{\aleph _0}\), and the number of logics having the FMP in them is either finite or \(2^{\aleph _0}\). (shrink)