Non-classical views about important issues in logic and its philosophy are a distinctive trait of Shahid Rahman's work. This volume has been designed, on the occasion of his 50th birthday, as a gathering place for unconventional approaches, original ideas and attempts to question well-established standards. Some of the world top philosophers and logicians contributed to a brilliant collection of papers, some of which doubtlessly leave their mark on the work to come in logic and in philosophy of formal (...) sciences. Contributors are: Philippe Balbiani, Diderik Batens, Johan van Benthem, Giacomo Bonanno, Walter A. Carnielli, Newton C. A. Da Costa, Michel Crubellier, Francisco A. Doria, Dov M. Gabbay, Olivier Gasquet, Gerhard Heinzmann, Andreas Herzig, Jaakko Hintikka, Justine Jacot, Reinhard Kahle, Erik C. W. Krabbe, Decio Krause, Franck Lihoreau, Kuno Lorenz, Ilkka Niiniluoto, Graham Priest, Stephen Read, Manuel Rebuschi, Greg Restall, Gabriel Sandu, Gerhard Schurz, Francois Schwarzentruber, Yaroslav Shramko, Goran Sundholm, John Symons, Christian Thiel, Nicolas Troquard, Tero Tulenheimo, Jean Paul Van Bendegem, Daniel Vanderveken, Yde Venema, Heinrich Wansing, Jan Wolenski and John Woods. (shrink)

The extensive research in logic conducted by using concepts and methods of game theory as documented in this collection of papers, allows to see dialogue logic in a number of new perspectives. This situation may gain further clarity by looking back to the inception of dialogue logic in the late fifties and early sixties.

The extensive research in logic conducted by using concepts and methods of game theory as documented in this collection of papers, allows to see dialogue logic in a number of new perspectives. This situation may gain further clarity by looking back to the inception of dialogue logic in the late fifties and early sixties.

There are several formal systems for persuasive dialogue. Dialogue systems are multi-Agent systems, and this contrasts with the general lack of any agency in standard logics other than in the case of epistemic and deontic logics. Dialogue systems have been called logics. A logic usually has a semantics and a proof system, and questions of soundness and completeness arise. Any dialogue conducted according to the rules of a dialogue logic is a complex process. (...) Dynamic Logic is a logic of processes, with a possible world semantics. This paper is a preliminary exploration of transforming the dialogues of dialogue logic into complex Dynamic Logic processes with emphasis on semantic models. The transformation gives rise to many questions, three of which are discussed. Dialogue logic includes commitment sets which behave in a way similar to belief sets and undergo changes during any dialogue. There are issues as to the relationship between belief and commitment, and whether the logics of belief change apply to commitment stores. There is also the issue of the logical nature of the evaluation of dialogues as legal or illegal. (shrink)

The first part of this paper presents asympathetic and critical examination of the approachof Shahid Rahman and Walter Carnielli, as presented intheir paper “The Dialogical Approach toParaconsistency”. In the second part, possibleextensions are presented and evaluated: (a) top-downanalysis of a dialogue situation versus bottom-up, (b)the specific role of ambiguities and how to deal withthem, and (c) the problem of common knowledge andbackground knowledge in dialogues. In the third part,I claim that dialogue logic is the best-suitedinstrument to analyse (...) paradoxes of the Sorites type.All these considerations lead to philosophicallyrelevant observations concerning principles of charityon the one hand, and compactness on the other. (shrink)

Stone-walling dialogues are exercises in structured non-cooperation. It is true that dialogue participants need to cooperate with one another and in ways sufficient to make possible the very dialogue they are now having. Beyond that there is room for non-cooperation on a scale that gives great offence to what we call the Goody Two-Shoes Model of argument. In this paper, we argue that non-cooperation dialogues have perfectly legitimate objectives and that in relation to those objectives they need not (...) be considered at all subpar to conversations that brim with sunny amity.Two categories of stone-walling non-cooperation dialogues are here examined. They are called MindClosed and NoEngage. They are exemplified by the following cases:1. Hostile Police Interrogation2. Judicial Cross-Examination3. Department Store Complaints Management4. Lakatosian Science5. Gödel's First Incompleteness Proof. (shrink)

In this paper, we define a class of dialogue games for Johansson’s minimal logic and prove that it corresponds to the validity of minimal logic. Many authors have stated similar results for intuitionistic and classical logic either with or without actually proving the correspondence. Rahman, Clerbout and Keiff [17] have already specified dialogues for minimal logic; however, they transformed it into Fitch-style natural deduction only. We propose a different specification for minimal logic with the (...) proof of correspondence between the existence of winning strategies for the Proponent in this class of games and the sequent calculus for minimal logic. (shrink)

Being a pragmatic and not a referential approach to semantics, dialogi-cal logic does not understand semantics as mapping names, propositions and relationships into the real world to obtain an abstract counterpart of it, but as dealing (handeln) with them in a particular way. This allows a very simple formulation of free logic the core of which can be expressed in a nutshell, namely: in an argumentation, it sometimes makes sense to restrict the introduction of singular terms in the (...) context of quantification to a formal use o f them. That is, the proponent is allowed to use a constant if f this constant has been explicitly conceded by the opponent. More technically, we show a new, dialogical way to build free logic systems fo r first-order logic with classical and intuitionistic features and present their corresponding tableaux. I. In tro d u ctio n I I. F r e e logics ON DIALOGUES A ND ONTOLOGY THE DIAL OGICAL APPROACH TO FREE LOGIC The proposition "God does not exist" contains a paradox sometimes referred to as Plato's beard: if God does not exist and the proposition should be true, standard referential semantics fo r quantified logic fails to give meaning to the name "God". But, given compositionality, since the meaning of a sentence is combined from the meanings o f its parts,-G o d d o e s not exist" does not evaluate. It is easy to see that related difficulties appear in every formula that contains singular terms. In standard logic, it is impossible to state that God is either good or evil without presupposing his existence, or that the round * My work on this article has been supported by the Fritz-Thyssen-Stiftung which I wish to thank expressly. (shrink)

This paper aims to develop the implications of logical expressivism for a theory of dialogue coherence. I proceed in three steps. Firstly, certain structural properties of cooperative dialogue are identified. Secondly, I describe a variant of the multi-agent natural deduction calculus that I introduced in Piwek (J Logic Lang Inf 16(4):403–421, 2007 ) and demonstrate how it accounts for the aforementioned structures. Thirdly, I examine how the aforementioned system can be used to formalise an expressivist account of (...) logical vocabulary that is inspired by Brandom (Making it explicit: reasoning, representing, and discursive commitment, 1994 ; Articulating reasons: an introduction to inferentialism, 2000 ). This account conceives of the logical vocabulary as a tool which allows speakers to describe the inferential practices which underlie their language use, i.e., it allows them to make those practices explicit. The rewards of this exercise are twofold: (1) We obtain a more precise account of logical expressivism which can be defended more effectively against the critique that such accounts lead to cultural relativism. (2) The formalised distinction between engaging in a practice and expressing it, opens the way for a revision of the theory of dialogue coherence. This revision eliminates the need for logically complex formulae to account for certain structural properties of cooperative dialogue. (shrink)

Dialogical logic is a game-theoretical approach to logic. Logic is studied with the help of certain games, which can be thought of as idealized argumentations. Two players, the Proponent, who puts forward the initial thesis and tries to defend it, and the Opponent, who tries to attack the Proponent’s thesis, alternately utter argumentative moves according to certain rules. For a long time the dialogical approach had been worked out only for classical and intuitionistic logic. The seven (...) papers of this dissertation show that this narrowness was uncalled for. The initial paper presents an overview and serves as an introduction to the other papers. Those papers are related by one central theme. As each of them presents dialogical formulations of a different non-classical logic, they show that dialogical logic constitutes a powerful and flexible general framework for the development and study of various logical formalisms and combinations thereof. As such it is especially attractive to logical pluralists that reject the idea of “the single correct logic”. The collection contains treatments of free logic, modal logic, relevance logic, connexive logic, linear logic, and multi-valued logic. (shrink)

An overview of different versions and applications of Lorenzen’s dialogue game approach to the foundations of logic, here largely restricted to the realm of manyvalued logics, is presented. Among the reviewed concepts and results are Giles’s characterization of Łukasiewicz logic and some of its generalizations to other fuzzy logics, including interval based logics, a parallel version of Lorenzen’s game for intuitionistic logic that is adequate for finite- and infinite-valued Gödel logics, and a truth comparison game for (...) infinite-valued Gödel logic. (shrink)

A philosophical movement, correctly called logical pragmatism, is growing up around the philosophy of W. V. O. Quine. Soviet scholars follow this development with clear and well-grounded understanding of the origins and tenets of the system. This essay continues the "dialogue" between contemporary Marxism-Leninism and logical pragmatism recommended by Soviet scholars.

The article mainly tries to discuss the dialogue between China and Western countries from the aspect of logic. There were three sources of logic, including formal logic in ancient Greek, logic in Early Qin of China as well as logic in ancient India. While, among all the schools in ancient China, Mohist and Virtuoso valued logic most. But as the rulers of Han Dynasty only paid their homage to Confucianism, the two schools gradually (...) sank, logic in Early Qin of China discontinued, without entering the main headstream of logic development worldwide. Later, logic in China had little influence on Chinese society although Indian logic was introduced in Tang Dynasty, a scholar-bureaucrat named Zhizao Li in Ming Dynasty, translated logic textbook Discussion of Name and Science, and German philosopher G.W. Leibniz explained Chinese changing theory with binary system. In the early 1900s, during the process of introducing western science, logic, regarded as the basis of science and a tool of scientific research, was highly valued by Chinese scholars, in fact, western logic entered China through two channels. After Chinese scholars learnt from western logic, they made their contribution to the development of logic. (shrink)

This very witty work, intended as an introductory text in logic, takes the form of a dialogue between teacher Penny and student Nickel, the dialogue illustrating Bierman's conception of the way to teach logic. But the book is perhaps of more value for its contributions to the philosophy of language, many of them admittedly "unfamiliar and unconventional." Among them: ascription of linguistic functions to physical objects with a consequent reduction of "referential" semantics to syntax; and the (...) beginnings of a "calculus of concepts" giving formal procedures for distinguishing sense from non-sense.—A. J. (shrink)

This paper tackles foundational issues regarding the justification of logical rules. It is argued that standard accounts from both proof-theoretical and semantical points of view do not su ffi ce to account for the justification of basic logical rules. By way of response, an analysis of logical inference as acts taking place in dialogical situations is provided. In turn, this makes way for an internal justification of logical rules at the termination of dialogue, that can be formalized in terms (...) of co-constructive logic for proof and refutation [author reference omitted]. (shrink)

The Barth–Krabbe–Hintikka–Hintikka Problem, independently raised by Barth and Krabbe and Hintikka and Hintikka Sherlock Holmes confronts modern logic: Toward a theory of information-seeking through questioning. Indiana University Press, Bloomington, 1983), is the problem of characterizing the strategic reasoning of the players of dialogical logic and game-theoretic semantics games from rational preferences rather than rules. We solve the problem by providing a set of preferences for players with bounded rationality and specifying strategic inferences from those preferences, for a variant (...) of logical dialogues. This solution is generalized to both game-theoretic semantics and orthodox dialogical logic. (shrink)

The purpose of this paper is to work toward an explicit logic and semantics for a game theoretically inspired theory of action. The purpose of the logic is to explicate the conceptual machinery implicit in the dialogue-game model of rational discourse developed in Carlson (1983).A variety of ideas and techniques of modal and philosophical logic are used to define a model structure that generalizes the game theoretical notion of a game in extensive form (von Neumann and (...) Morgenstern, 1944). Relative to this model structure, semantic characterizations are given to the action-theoretic notions oftime, possibility, belief, preference, ability, intention, action, andrationality. The unification of these characterizations under the game-theoretical paradigm leads to insights about the logical interdependences between these concepts. (shrink)

Dialogue theory, although it has ancient roots, was put forward in the 1970s in logic as astructure that can be useful for helping to evaluate argumentation and informal fallacies.Recently, however, it has been taken up as a broader subject of investigation in computerscience. This paper surveys both the historical and philosophical background of dialoguetheory and the latest research initiatives on dialogue theory in computer science. The main components of dialogue theory are briefly explained. Included is a (...) classification of the main types of dialogue that, it is argued, should provide the central focus for studying many important dialogue contexts in specific cases. Following these three surveys, a concluding prediction is made about the direction dialogue theory is likely to take in the next century, especially in relation to the growing field of communication studies. (shrink)

This article presents a case of the application of Buddhist yinming logic in a public debate between Buddhists and Daoists at the court of Emperor Tang Gaozong, as recorded by Daoxuan in his Ji Gujin Fo Dao Lunheng. The application was successful in the sense that the Buddhist vanquished his Daoist opponent. Yet, yinming logic was not used in other debates against Daoists, not even by Buddhists trained in this particular logic. Why? Looking for answers to this (...) question, the article argues for the importance of common analytical ground in inter-religious, and by extension intercultural debate. (shrink)

The article focuses on the New Rhetoric’s concept of quasi-logical arguments imitating logical or mathematical demonstrations, and examines it from point of view of pragma-dialectics as a device contributing towards resolving the difference of opinion. It is shown that the category of quasi-logical arguments cannot be considered as an argument scheme or a united type of strategic maneuvering. It is suggested to consider the category of quasi-logical arguments as a cluster of specific strategic maneuvers increasing the efficiency of arguments under (...) certain circumstances. This approach is demonstrated in a case study of pragma-dialectical analysis of the quasi-logical scheme of probability. (shrink)

Develops a logical analysis of dialogue in which two or more parties attempt to advance their own interests. It includes a classification of the major types of dialogues and a discussion of several important informal fallacies.

We describe how Intuitionistic Linear Logic can be used to provide a unified logical account for agents to find and execute plans. This account supports the modelling of agent interaction, including dialogue; allows agents to be robust to unexpected events and failures; and supports significant reuse of agent specifications. The framework has been implemented and several case studies have been considered. Further applications include human–computer interfaces as well as agent interaction in the semantic web.