In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Łukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all instances of the game played on the same formula, may be interpreted as derivations in a corresponding proof system. In (...) particular, such strategies mirror derivations in a hypersequent calculus developed in recent work on the proof theory of Łukasiewicz logic. (shrink)

Motivated by aspects of reasoning in theories of physics, Robin Giles defined a characterization of infinite valued Łukasiewicz logic in terms of a game that combines Lorenzen-style dialogue rules for logical connectives with a scheme for betting on results of dispersive experiments for evaluating atomic propositions. We analyze this game and provide conditions on payoff functions that allow us to extract many-valued truth functions from dialogue rules of a quite general form. Besides finite and infinite valued Łukasiewicz logics, also Meyer (...) and Slaney’s Abelian logic and Cancellative Hoop Logic turn out to be characterizable in this manner. (shrink)

We introduce a game for Gödel logic where the players’ interaction stepwise reduces claims about the relative order of truth degrees of complex formulas to atomic truth comparison claims. Using the concept of disjunctive game states this semantic game is lifted to a provability game, where winning strategies correspond to proofs in a sequents-of-relations calculus.

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.

A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the (...) number of truth values, and it is shown that this bound is tight. (shrink)

We present an interdisciplinary approach to argumentation combining logical, probabilistic, and psychological perspectives. We investigate logical attack principles which relate attacks among claims with logical form. For example, we consider the principle that an argument that attacks another argument claiming A triggers the existence of an attack on an argument featuring the stronger claim A ∧ B. We formulate a number of such principles pertaining to conjunctive, disjunctive, negated, and implicational claims. Some of these attack principles seem to be prima (...) facie more plausible than others. To support this intuition, we suggest an interpretation of these principles in terms of coherent conditional probabilities. This interpretation is naturally generalized from qualitative to quantitative principles. Specifically, we use our probabilistic semantics to evaluate the rationality of principles which govern the strength of argumentative attacks. In order to complement our theoretical analysis with an empirical perspective, we present an experiment with students of the TU Vienna ( n = 139) which explores the psychological plausibility of selected attack principles. We also discuss how our qualitative attack principles relate to well-known types of logical argumentation frameworks. Finally, we briefly discuss how our approach relates to the computational argumentation literature. (shrink)

Vagueness is one of the most persistent and challenging topics in the intersection of philosophy and logic. At least five other noteworthy books on vagueness have been written by philosophers since 1991 [2, 6, 11, 12, 15]. A (necessarily incomplete) bibliography that has been compiled for the Arché project Vagueness: its Nature and Logic (2004-2006) of the University of St Andrews lists more than 350 articles and books on vagueness until 2005.1 Many new and interesting contributions have appeared since. The (...) book under review is much more than yet another addition to this prolific discourse. Nicholas Smith manages to tackle two different tasks that are potentially in tension. On the one hand, he provides a comprehensive, systematic and well written account of various approaches to vagueness that have been debated so far. On the other hand, Smith carefully explains and defends his own theory of vagueness, called fuzzy plurivaluationism. Given the complex and almost unsurmountably large amount of relevant literature and the fact that theories of vagueness based on fuzzy logic have almost universally been rejected by philosophers so far this is no simple feat. In the comments below, I will largely follow the structure of book. If along the way I cannot resist to make side remarks or even take issue with some of.. (shrink)

We explore different ways to generalize Hintikka’s classic game theoretic semantics to a many-valued setting, where the unit interval is taken as the set of truth values. In this manner a plethora of characterizations of Łukasiewicz logic arise. Among the described semantic games is Giles’s dialogue and betting game, presented in a manner that makes the relation to Hintikka’s game more transparent. Moreover, we explain a so-called explicit evaluation game and a ‘bargaining game’ variant of it. We also describe a (...) recently introduced backtracking game as well as a game with random choices for Łukasiewicz logic. (shrink)

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and (...) the exclusion of the opposite truth value describe the same situation.). (shrink)

A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.

Vague language and corresponding models of inference and information processing is an important and challenging topic as witnessed by a number of recent monographs and collections of essays devoted to the topic. This volume collects fifteen papers, the majority of which originated with talks presented at the conference "Logical Models of Reasoning with Vague Information ", September 14-17, 2009, in Čejkovice, that initiated a EUROCORES/LogICCC project with the same title. At least two features set the current volume apart from other (...) texts: first, the interdisciplinary nature of the topic is nicely reflected by the wide range of interests of the authors, who include philosophers, linguists, logicians, as well as mathematicians and computer scientists. Secondly, all the papers are accompanied by comments written by other authors and a few outside experts. These comments and corresponding replies by the authors document the very lively ongoing debate on adequate models of vague language. (shrink)

Spacetime as we know and love it is lost in most approaches to quantum gravity. For many of these approaches, as inchoate and incomplete as they may be, one of the main challenges is to relate what they take to be the fundamental non-spatiotemporal structure of the world back to the classical spacetime of GR. The present essay investigates how spacetime is lost and how it may be regained in one major approach to quantum gravity, loop quantum gravity.

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.

The problem of free will as it is know in Western philosophical traditions is hardly known in China. Considering how central the problem is in the West, this is a remarkable fact. We try to explain this, and we offer insights into discussions within Chinese traditions that we think are related, not historically but regarding the issues discussed. Thus we introduce four central Chinese concepts, namely: (1) xīn 心 (heart, heart-mind), (2) xìng 性 (human nature, characteristic tendencies, inborn capacity), (3) (...) mìng 命 (lifespan, fate, command, allotment, endowment), and (4) zìrán 自然 (self-so, so of itself, nature, spontaneity), and we indicate how these concepts and their discussions can be related to discussions on free will. (shrink)

_Making Sense of Tantric Buddhism_ fundamentally rethinks the nature of the transgressive theories and practices of the Buddhist Tantric traditions, challenging the notion that the Tantras were "marginal" or primitive and situating them instead--both ideologically and institutionally--within larger trends in mainstream Buddhist and Indian culture. Critically surveying prior scholarship, Wedemeyer exposes the fallacies of attributing Tantric transgression to either the passions of lusty monks, primitive tribal rites, or slavish imitation of Saiva traditions. Through comparative analysis of modern historical narratives--that depict (...) Tantrism as a degenerate form of Buddhism, a primal religious undercurrent, or medieval ritualism--he likewise demonstrates these to be stock patterns in the European historical imagination. Through close analysis of primary sources, Wedemeyer reveals the lived world of Tantric Buddhism as largely continuous with the Indian religious mainstream and deploys contemporary methods of semiotic and structural analysis to make sense of its seemingly repellent and immoral injunctions. Innovative, semiological readings of the influential _Guhyasamaja Tantra_ underscore the text's overriding concern with purity, pollution, and transcendent insight--issues shared by all Indic religions--and a large-scale, quantitative study of Tantric literature shows its radical antinomianism to be a highly managed ritual observance restricted to a sacerdotal elite. These insights into Tantric scripture and ritual clarify the continuities between South Asian Tantrism and broader currents in Indian religion, illustrating how thoroughly these "radical" communities were integrated into the intellectual, institutional, and social structures of South Asian Buddhism. (shrink)

_Making Sense of Tantric Buddhism_ fundamentally rethinks the nature of the transgressive theories and practices of the Buddhist Tantric traditions, challenging the notion that the Tantras were "marginal" or primitive and situating them instead -- both ideologically and institutionally -- within larger trends in mainstream Buddhist and Indian culture. Critically surveying prior scholarship, Wedemeyer exposes the fallacies of attributing Tantric transgression to either the passions of lusty monks, primitive tribal rites, or slavish imitation of Saiva traditions. Through comparative analysis of (...) modern historical narratives -- that depict Tantrism as a degenerate form of Buddhism, a primal religious undercurrent, or medieval ritualism -- he likewise demonstrates these to be stock patterns in the European historical imagination. Through close analysis of primary sources, Wedemeyer reveals the lived world of Tantric Buddhism as largely continuous with the Indian religious mainstream and deploys contemporary methods of semiotic and structural analysis to make sense of its seemingly repellent and immoral injunctions. Innovative, semiological readings of the influential _Guhyasamaja Tantra_ underscore the text's overriding concern with purity, pollution, and transcendent insight -- issues shared by all Indic religions -- and a large-scale, quantitative study of Tantric literature shows its radical antinomianism to be a highly managed ritual observance restricted to a sacerdotal elite. These insights into Tantric scripture and ritual clarify the continuities between South Asian Tantrism and broader currents in Indian religion, illustrating how thoroughly these "radical" communities were integrated into the intellectual, institutional, and social structures of South Asian Buddhism. (shrink)

De differentia nexus rerum sapientis et fatalis necessitatis -- Monitum ad commentationem luculentam de differentia nexus rerum sapientis et fatalis necessitatis.

Mémoire de Mons. Lange contre cette philosophie -- Réponse préliminaire d'un auteur anonimeà ce mémoire -- Sommaire de la réponse de Mr. Wolf mȩme avec un avis au lecteur de l'histoire de ce nouveau différend.

Cognitive impenetrability (CI) of a large part of visual perception is taken for granted by those of us in the field of computational vision who attempt to recover descriptions of space using geometry and statistics as tools. These tools clearly point out, however, that CI cannot extend to the level of structured descriptions of object surfaces, as Pylyshyn suggests. The reason is that visual space – the description of the world inside our heads – is a nonEuclidean curved space. As (...) a consequence, the only alternative for a vision system is to develop several descriptions of space–time; these are representations of reduced intricacy and capture partial aspects of objective reality. As such, they make sense in the context of a class of tasks/actions/plans/purposes, and thus cannot be cognitively impenetrable. (shrink)

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www<dot>beyondspacetime<dot>net.) This chapter introduces causal set theory and identifies and articulates a 'problem of space' in this theory.

Keine ausführliche Beschreibung für "Ethik und Technik" verfügbar.

Des Herrn Doct. und Prof. Joachim Langens, oder, Der Theologischen Facultaet zu Halle Anmerckungen über des Herrn Hoff-Raths und Professor Christian Wolffens Metaphysicam ... nebst beygefügter Hr. Hoff-R. und Prof. Christian Wolffens gründlicher Antwort -- Herrn D. Joh. Francisci Buddei S.S. Theol. P.P.O. zu Jena Bedencken über die Wolffianische Philosophie, mit Anmerckungen erläutert von Christian Wolffen.

We present an interdisciplinary approach to study systematic relations between logical form and attacks between claims in an argumentative framework. We propose to generalize qualitative attack principles by quantitative ones. Specifically, we use coherent conditional probabilities to evaluate the rationality of principles which govern the strength of argumentative attacks. Finally, we present an experiment which explores the psychological plausibility of selected attack principles.