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Paraconsistency, Evidence, and Abduction

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Handbook of Abductive Cognition

Abstract

This chapter gathers together and sums up the recent work on technical and philosophical aspects of logics of evidence and truth (LETs) through a study of the logics LETF and LETK, including an application of the latter to the problem of abduction. LETF is a paracomplete and paraconsistent sentential logic equipped with a unary operator ∘ that divides the sentences of the language into two groups: one subjected to classical logic and the other subjected to the logic of first-degree entailment (FDE), also known as Belnap-Dunn four-valued logic. The chapter discusses the intuitive intended interpretation of LETF in terms of positive and negative evidence, and shows how LETF can be interpreted in terms of reliable and unreliable information. It then presents natural deduction systems, valuation semantics, and analytic tableau system for both LETF and LETK, which extends LETF with a classical implication connective. Finally, it shows how LETK and its first-order extension QLETK can be applied to the problem of abduction by means of tableaux that indicate possible solutions for abductive problems. The chapter also includes an appendix that contains some general remarks on valuation semantics, Kripke-style semantics for both LETF and LETK, and a probabilistic semantics for LETF.

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Author information

Authors and Affiliations

  1. Department of Philosophy, Federal University of Minas Gerais, Belo Horizonte, Brazil

    A. Rodrigues

  2. Department of Philosophy and Centre for Logic, Epistemology and the History of Science, University of Campinas, Campinas, Brazil

    H. Antunes

  3. Department of Philosophy, Federal University of Bahia, Salvador, Brazil

    M. E. Coniglio

  4. Centre for Logic, Epistemology and the History of Science, and School of Technology, Rua Paschoal Marmo, University of Campinas, Limeira, Brazil

    J. Bueno-Soler

  5. Centre for Logic, Epistemology and the History of Science, Rua Sérgio Buarque de Holanda, University of Campinas, Campinas, Brazil

    W. Carnielli

Authors
  1. A. Rodrigues
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  2. M. E. Coniglio
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  3. H. Antunes
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  4. J. Bueno-Soler
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  5. W. Carnielli
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Editor information

Editors and Affiliations

  1. Department of Humanities, University of Pavia, Pavia, Italy

    Lorenzo Magnani

Section Editor information

  1. Institute for Philosophical Research, National Autonomous University of Mexico, Mexico City, Mexico

    Atocha Aliseda

  2. Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México http://www.filosoficas.unam.mx/~atocha/home.html

    Atocha Aliseda

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Rodrigues, A., Coniglio, M.E., Antunes, H., Bueno-Soler, J., Carnielli, W. (2022). Paraconsistency, Evidence, and Abduction. In: Magnani, L. (eds) Handbook of Abductive Cognition. Springer, Cham. https://doi.org/10.1007/978-3-030-68436-5_27-1

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  • DOI: https://doi.org/10.1007/978-3-030-68436-5_27-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68436-5

  • Online ISBN: 978-3-030-68436-5

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