This edited volume collects essays on the four-valued logic known as Belnap-Dunn logic, or first-degree entailment logic. It also looks at various formal systems closely related to it. These include the strong Kleene logic and the Logic of Paradox. Inside, readers will find reprints of seminal papers written by the fathers of the field: Nuel Belnap and Michael Dunn. In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay (...) by Dunn. Besides the original, monumental papers, the book also includes research by leading scholars. They consider the extraordinary importance of Belnap-Dunn logic from several perspectives. They look at how, philosophically, it has served as a basic system of inconsistency-tolerant reasoning, as the core of underlying logics for theories based on dialetheism, and, more recently, for theories based on Buddhist philosophy. Coverage also explores its contributions to computer science, such as knowledge representation and information processing. This mix of seminal papers and insightful analysis by top scholars offers readers a comprehensive outlook on Belnap-Dunn logic and its related expansions, which have been agenda setting for the debate on philosophical logic as well as philosophy of logic. The book will also enhance further discussion on the philosophical issues related to nonclassical logics in general. (shrink)

Excerpt from Die Prinzipien der Mechanik in Neuem Zusammenhange Dargestellt Wahl eines Berufs entschliefsen mufste, wahlte er den des Ingenieurs. Es scheint, dafs die auch in spateren Jahren als ein charakteristischer Grundzug seines Wesens hervor tretende Bescheidenheit ihn an seiner Begabung fur theore tische Wissenschaft zweifeln liefs, und dafs er sich bei der Beschaftigung mit seinen geliebten mechanischen Arbeiten des Erfolges sicherer fuhlte, weil er deren Tragweite schon damals ausreichend verstand. Vielleicht hat ihn auch die in seiner Vaterstadt herrschende, mehr (...) dem Praktischen zugeneigte Sinnesweise beeinflufst. Ubrigens beobachtet man nicht selten diese Art zaghafter Bescheidenheit gerade bei jungen Leuten von hervorragenden Anlagen. Sie haben wohl eine deutliche Vorstellung von den Schwierigkeiten, die vor der Erreichung des ihnen vorschwebenden hohen Zieles zu uberwinden sind, und mussen ihre Krafte erst praktisch erprobt haben, ehe sie das zu ihrem schweren Werke notige Selbstvertrauen ge winnen. Aber auch in ihrer spateren Entwickelung pflegen reich veranlagte Naturen um so unzufriedener mit ihren eigenen Werken zu sein je hoher ihre Fahigkeiten und ihre Ideale reichen. Die Begabtesten erreichen offenbar nur des halb das Hochste, weil sie am empfindlichsten gegen jede Un vollkommenheit sind, und am unermudlichsten an deren Beseitigung arbeiten. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

According to Suszko’s Thesis, there are but two logical values, true and false. In this paper, R. Suszko’s, G. Malinowski’s, and M. Tsuji’s analyses of logical twovaluedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation. [A] fundamental problem concerning many-valuedness is to know what it really is. [13, p. 281].

Connexive logic has room for two pairs of universal and particular quantifiers: one pair, |$\forall $| and |$\exists $|⁠, are standard quantifiers; the other pair, |$\mathbb{A}$| and |$\mathbb{E}$|⁠, are unorthodox, but we argue, are well-motivated in the context of connexive logic. Both non-standard quantifiers have been introduced previously, but in the context of connexive logic they have a natural semantic and proof-theoretic place, and plausible natural language readings. The results are logics that are negation inconsistent but non-trivial.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

Zusammensetzung des Körpers.--Die sinnliche Wahrnehmung.--Der Mikrokosmos (der Mensch eine kleine Welt)--Embryologie, Astrologie.--Die Theilseele.--Die Grenze des menschlichen Wissens.--Leben und Tod.--Schmerz und Lust.--Ton, Laut, Sprache.

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem''s modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap''s display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to (...) be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules. (shrink)

Neinsagen ist die Formel des Protestes. In einer Welt, die zu Protesten Anlaß bietet, scheint es nicht überflüssig, diese Formel zu untersuchen.

In this paper functional completeness results are obtained for certain positive and constructive propositional logics associated with a Tarski-type structured consequence relation as defined by Gabbay.

In this paper we elaborate a conception of entailment based on what we call the Ackermann principle, which explicates valid entailment through a logical connection between sentences depending on their informational content. We reconstruct Dunn’s informational semantics for entailment on the basis of Restall’s approach, with assertion and denial as two independent speech acts, by introducing the notion of a ‘position description’. We show how the machinery of position descriptions can effectively be used to define the positive and the negative (...) information carried by sentences of a given language and to present a formalized version of the Ackermann principle as an inclusion relationship between the informational contents of the conclusions and the premises of a valid entailment. Being so interpreted, the entailment relation exhibits certain properties, including the property of transitivity. Whereas properties such as Anderson and Belnap’s variable sharing property or Parry’s proscriptive principle are normally presented as imposing a relevance requirement on valid entailment, the suggested formalization of the Ackermann principle supports all of Gentzen’s structural rules, including weakening, a rule that is normally given up in sequent-style proof systems for relevance logics. In this way we propose an Ackermann-inspired explication of the nature of entailment as a relation between the informational contents of sentences. (shrink)

Leibniz hat sein Projekt einer Scientia generalis, die das gesamte Wissen seiner Zeit in einer Enzyklopädie komprimieren sollte, vor seinen Zeitgenossen geheim gehalten. Bei einzelnen Briefpartnern versuchte er, Verständnis für Thesen seiner Metaphysik zu finden, ohne zu viel davon preiszugeben. Heinrich Schepers will in seinen Beiträgen dem nahe kommen, was Leibniz' wahre Metaphysik ausmacht. Die Perzeption und der Appetitus sind die spontanen Handlungen, mit denen sich die Individuen selbst konstituieren. Die Kompatibilität ist die Relation, die sie auf die vielen (...) möglichen Welten verteilt. Die sich dabei herausstellenden Grade der Perfektion machen die Wahl der besten unter ihnen möglich. Aus den spontanen Handlungen der einfachen Substanzen leitet Leibniz seine Begriffe von Raum und Zeit ab. Tragend für diese Theorie ist sein konzeptualistischer Gottesbegriff, demzufolge nicht allein die Essenzen, sondern alles Denkbare in Form vollausgebildeter Subjekte materiell Gottes Verstand ausmachen. (shrink)

With the deep economic crisis we face since 2008 also the interest in Marxian theories increased worldwide. This was not really surprising: while in Marx’s economic theory crises play an important role, they are nearly neglected in mainstream economics. They appear there as mere accidents, which could be prohibited by flexible markets (this is the belief of neoclassical economists) or by an appropriate economic policy (the belief of the Keynesians). But talking about Marxian economic theory, we should always have in (...) mind, that there is a certain development in Marx’s thinking as well as there are certain ambivalences in basic theoretical concepts. In traditional Marxism, which mostly tried to present Marxian theory as a complete and perfect building, especially such ambivalences were often negIected or even denied. In the following I will give a short overview about the main stages of Marx’s theoretical development, and then I will focus on the ambivalences of Marx’s mature theoretical work. (shrink)

.Es wird über eine Untersuchung zur Forschungsmethodik der Wirtschaftsinformatik berichtet. Untersuchungsziel war es, den Stellenwert von Forschungsmethodik in der Wirtschaftsinformatik zu bestimmen und den Befund dazu zu erklären. Das Untersuchungsziel wurde mit einer Stichprobenanalyse verfolgt. Als Stichprobe wurden die vierzehn Jahrgänge 1990 bis 2003 der Zeitschrift WIRTSCHAFTSINFORMATIK verwendet. Im Ergebnis wird festgestellt, dass die Wirtschaftsinformatik erhebliche forschungsmethodische Anstrengungen unternehmen muss, wenn sie auf dem Weg von einer Kunstlehre zur Wissenschaft zügig vorankommen will.