Topic
Paraconsistent logic
About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.
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01 Jan 2002
TL;DR: The main content of as discussed by the authors is a new foundation for intuitionistic logic, based on an analysis of argumentative processes as codified in the concepts of a dialogue and a strategy for dialogues.
Abstract: The principal content of this article is a (new) foundation for intuitionistic logic, based on an analysis of argumentative processes as codified in the concepts of a dialogue and a strategy for dialogues. This work is presented in Section 3. A general historical introduction is given in Section2. Since already there the reader will need to know exactly what a dialogue and a strategy shall be, these basic concepts are defined in the (purely technical) Section 1.
104 citations
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TL;DR: A new stand regarding the relations between logic and ontology is defended, and some first order heterodox logics as genuine alternatives to classical logic are accepted.
Abstract: In view of the present state of development of non classical logic, especially of paraconsistent logic, a new stand regarding the relations between logic and ontology is defended In a parody of a dictum of Quine, my stand May be summarized as follows. To be is to be the value of a variable a specific language with a given underlying logic Yet my stand differs from Quine’s, because, among other reasons, I accept some first order heterodox logics as genuine alternatives to classical logic I also discuss some questions of non classical logic to substantiate my argument, and suggest that may position complements and extends some ideas advanced by L Apostel.
104 citations
TL;DR: This paper has attempted to cover the basic material on natural deduction, sequent calculus, and typed λ-calculus, but also to provide an introduction to Girard's linear logic, one of the most exciting developments in logic these past six years.
103 citations
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TL;DR: A comparative study of various model-theoretic treatments of negation can be found in this paper, where a defence of Dialetheic Theory of Negation is presented.
Abstract: Preface. Part I: Models, Relevance and Impossibility. Negation: Two Points of View A. Avron. A Comparative Study of Various Model-Theoretic Treatments of Negation: A History of Formal Negation J.M. Dunn. Negation in Relevant Logics (How I Stopped Worrying and Learned to Love the Routley Star) G. Restall. Negation in the Light of Modal Logic K. Dosen. Part II: Paraconsistency, Partiality and Logic Programming. Negation and Contradiction D. Gabbay, A. Hunter. What not? A Defence of Dialetheic Theory of Negation G. Priest. Partial Logics with Two Kinds of Negation as a Foundation for Knowledge-Based Reasoning H. Herre, et al. From Here to There: Stable Negation in Logic Programming D. Pearce. Part III: Absurdity, Falsity and Refutability. Antirealism and Falsity M. Hand. Negation, Absurdity and Contrariety N. Tennant. Negation as Falsity: A Reply to Tennant H. Wansing. Part IV: Negations, Natural Language and The Liar. Models for Non-Boolean Negations in Natural Languages Based on Aspect Analysis M. La Palme Reyes, et al. Negation, Denial and Language Change in Philosophical Logic J. Tappenden. What is That Item Designated Negation? R. Sylvan. Index.
103 citations