In abstract argumentation, each argument is regarded as atomic. There is no internal structure to an argument. Also, there is no specification of what is an argument or an attack. They are assumed to be given. This abstract perspective provides many advantages for studying the nature of argumentation, but it does not cover all our needs for understanding argumentation or for building tools for supporting or undertaking argumentation. If we want a more detailed formalization of arguments than is available with (...) abstract argumentation, we can turn to structured argumentation, which is the topic of this special issue of Argument and Computation. In structured argumentation, we assume a formal language for representing knowledge and specifying how arguments and counterarguments can be constructed from that knowledge. An argument is then said to be structured in the sense that normally, the premises and claim of the argument are made explicit, and the relationship between the premises and claim is formally defined (for instance, using logical entailment). In this introduction, we provide a brief overview of the approaches covered in this special issue on structured argumentation. (shrink)

Dung’s (1995) argumentation framework takes as input two abstract entities: a set of arguments and a binary relation encoding attacks between these arguments. It returns acceptable sets of arguments, called extensions, w.r.t. a given semantics. While the abstract nature of this setting is seen as a great advantage, it induces a big gap with the application that it is used to. This raises some questions about the compatibility of the setting with a logical formalism (i.e., whether it is possible to (...) instantiate it properly from a logical knowledge base), and about the significance of the various semantics in the application context. In this paper we tackle the above questions. We first propose to fill in the previous gap by extending Dung’s (1995) framework. The idea is to consider all the ingredients involved in an argumentation process. We start with the notion of an abstract monotonic logic which consists of a language (defining the formulas) and a consequence operator. We show how to build, in a systematic way, arguments from a knowledge base formalised in such a logic. We then recall some basic postulates that any instantiation should satisfy. We study how to choose an attack relation so that the instantiation satisfies the postulates. We show that symmetric attack relations are generally not suitable. However, we identify at least one ‘appropriate’ attack relation. Next, we investigate under stable, semi-stable, preferred, grounded and ideal semantics the outputs of logic-based instantiations that satisfy the postulates. For each semantics, we delimit the number of extensions an argumentation system may have, characterise the extensions in terms of subsets of the knowledge base, and finally characterise the set of conclusions that are drawn from the knowledge base. The study reveals that stable, semi-stable and preferred semantics either lead to counter-intuitive results or provide no added value w.r.t. naive semantics. Besides, naive semantics either leads to arbitrary results or generalises the coherence-based approach initially developed by Rescher and Manor (1970). Ideal and grounded semantics either coincide and generalise the free consequence relation developed by Benferhat, Dubois, and Prade (1997), or return arbitrary results. Consequently, Dung’s (1995) framework seems problematic when applied over deductive logical formalisms. (shrink)

The study of logic usually focuses on either the proof theoretic or the model theoretic properties of logic. Yet the pragmatics of logic is often ignored. In this paper we would like to demonstrate that a logic can be practical in the sense that it can assist us in evaluating and measuring the amount of information in an inconsistent set of data. The underlying notion of information is inspired by Shannon's communication theory. It defines the amount of information of a (...) message in terms of the probability of the message being true. The logic presented here is the paraconsistent logic QC. As such QC logic can be seen as an analytical tool for evaluating data. (shrink)

We investigate two formalizations of Optimality Theory, a successful paradigm in linguistics.We first give an order-theoretic counterpart for the data and processinvolved in candidate evaluation.Basically, we represent each constraint as a function that assigns every candidate a degree of violation.As for the second formalization, we define (after Samek-Lodovici and Prince) constraints as operations that select the best candidates out of a set of candidates.We prove that these two formalizations are equivalent (accordingly, there is no loss of generality with using violation (...) marks and dispensing with them is only apparent).Importantly, we show that the second formalization is equivalent with a class of operations over sets of formulas in a given logical language.As a result, we prove that Optimality Theory can be characterized by certain cumulative logics.So, applying Optimality Theory is shown to be reasoning by the rules of cumulative logics. (shrink)

This paper investigates when two abstract logic-based argumentation systems are equivalent. It defines various equivalence criteria, investigates the links between them, and identifies cases where two systems are equivalent with respect to each of the proposed criteria. In particular, it shows that under some reasonable conditions on the logic underlying an argumentation system, the latter has an equivalent finite subsystem, called core. This core constitutes a threshold under which arguments of the system have not yet attained their final status and (...) consequently adding a new argument may result in status change. From that threshold, the statuses of all arguments become stable. (shrink)

This paper aims at laying some foundations of a logic of argumentation in which arguments, as well as attacks and supports among arguments are all defined in a unifying formalism. In the latter, an argument is denoted as a pair displaying a reason and a conclusion but no condition is required to hold relating the reason to the conclusion. We introduce a series of inference rules relating arguments and show how the resulting system captures important features of argumentation that hitherto (...) have not been captured by existing formalisms. (shrink)

Malament (Noûs 11:293–300, 1977) proved a certain uniqueness theorem about standard synchrony, also known as Poincaré-Einstein simultaneity, which has generated many commentaries over the years, some of them contradictory. We think that the situation called for some clarification. After reviewing and discussing some of the literature involved, we prove two results which, hopefully, will help clarifying this debate by filling the gap between the uniquess of Malament’s theorem, which allows the observer to use very few tools, and the complete arbitrariness (...) of a time coordinate in full-fledged Relativity theory. In the spirit of Malament’s theorem, and in opposition to most of its commentators, we emphasize explicit definability of simultaneity relations, and give only constructive proofs. We also explore what happens when we reduce to “purely local” data with respect to an observer. (shrink)

This book reveals how, when, where and why vitalism and its relationship to new scientific theories, philosophies and concepts of energy became seminal from the fin de siècle until the Second World War for such Modernists as Sophie Tauber-Arp, Hugo Ball, Juliette Bisson, Eva Carrière, Salvador Dalì, Robert Delaunay, Marcel Duchamp, Edvard Munch, Picasso, Yves Tanguy, Gino Severini and John Cage. For them Vitalism entailed the conception of life as a constant process of metamorphosis impelled by the free flow of (...) energies, imaginings, intuition and memories, unconstrained by mechanistic materialism and chronometric imperatives, to generate what the philosopher Henri Bergson aptly called Creative Evolution. Following the three main dimensions of Vitalist Modernism, the first part of this book reveals how biovitalism at the fin de siècle entailed the pursuit of corporeal regeneration through absorption in raw nature, wholesome environments, aquatic therapies, electromagnetism, heliotherapy, modern sports, particularly rugby; water sports, the Olympic Games and physical culture to energize the human body and vitalize its life force. This is illuminated by artists as geoculturally diverse as Gustave Caillebotte, Thomas Eakins, Munch and Albert Gleizes. The second part illuminates how simultaneously vitalism became aligned with anthroposophy, esotericism, magnetism, occultism, parapsychology, spiritism, theosophy and what Bergson called "psychic states", alongside such new sciences as electromagnetism, radiology and the Fourth Dimension, as captured by such artists as Juliette Bisson, Giacomo Balla, Albert Besnard, Umberto Boccioni, Eva Carrière, John Gerrard Keulemans, László Mohology-Nagy, James Tissot, Albert von Schrenck Notzing and Picasso. During and after the devastation of the First World War, the third part explores how Vitalism, particularly Bergson's theory of becoming, became associated with Dadaist, Neo-Dadaist and Surrealist notions of amorality, atemporality, dysfunctionality, entropy, irrationality, inversion, negation and the nonsensical captured by Hans Arp, Charlie Chaplin, Theo Van Doesburg, Kazimir Malevich, Kurt Schwitters and Vladimir Tatlin alongside Cage's concept of Nothing. After investigating the widespread engagement with Bergson's philosophies, Vitalism and art by Anarchists, Marxists and Communists during and after the First World War, it concludes with the official rejection of Bergson and any form of Vitalism in the Soviet Union under Stalin. This book will be of vital interest to gallery, exhibition and museum curators and visitors plus readers and scholars working in art history, art theory, cultural studies, modernist studies, occult studies, European art and literature, health, histories of science, philosophy, psychology, sociology, sport studies, heritage studies, museum studies and curatorship. (shrink)

This paper defends the use of possibility and necessity models based on the Logics of Formal Inconsistency, taking advantage of their expressivity in terms of the notions of consistency and inconsistency. The present proposal directly generalizes the approach of Besnard and Lang, whose main guidelines we borrow here. Some basic properties of possibility and necessity functions over the Logics of Formal Inconsistency are obtained and it is shown, by revisiting a paradigmatic example, how paraconsistent possibility and necessity reasoning can, (...) in general, attain realistic models for artificial judgement. We will call such models credal calculi, emphasizing some of their appealing consequences. (shrink)