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Formal (In)consistency, Abduction and Modalities

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Springer Handbook of Model-Based Science

Part of the book series: Springer Handbooks ((SHB))

Abstract

This chapter proposes a study of philosophical and technical aspects of logics of formal inconsistency (GlossaryTerm

LFI

s), a family of paraconsistent logics that have resources to express the notion of consistency inside the object language. This proposal starts by presenting an epistemic approach to paraconsistency according to which the acceptance of a pair of contradictory propositions A and \(\neg A\) does not imply accepting both as true. It is also shown how LFIs may be connected to the problem of abduction by means of tableaux that indicate possible solutions for abductive problems. The connection between the notions of modalities and consistency is also worked out, and some LFIs based on positive modal logics (called anodic modal logics), are surveyed, as well as their extensions supplied with different degrees of negations (called cathodic modal logics). Finally, swap structures are explained as new and interesting semantics for the LFIs, and shown to be as a particular important case of the well-known possible-translations semantics (GlossaryTerm

PTS

).

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Abbreviations

AI:

artificial intelligence

bd:

basic property of determinedness

CPL+:

Positive classical propositional logic

classical positive propositional logic

CPL:

classical propositional logic

DAT:

derivability adjustment theorem

LDI:

logics of deontic (in)consistency

LET K :

the logic of evidence and truth based on CPL+

LFI:

logics of formal inconsistency

PTS:

possible-translations semantics

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Author information

Authors and Affiliations

  1. School of Technology, University of Campinas, Rua Paschoal Marmo 1888, SP 13484-332, Limeira, Brazil

    Juliana Bueno-Soler

  2. Centre for Logic, Epistemology and the History of Science, University of Campinas, Rua Sérgio Buarque de Holanda, 251 Barão Geraldo, DEP, SP 13083-85, Campinas, Brazil

    Walter Carnielli & Marcelo E. Coniglio

  3. Department of Philosophy, Federal University of Minas Gerais, Av. Antonio Carlos 6627, FAFI CH, 31270-901, Pampulha, Belo Horizonte, Brazil

    Abilio Rodrigues Filho

Authors
  1. Juliana Bueno-Soler
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  2. Walter Carnielli
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  3. Marcelo E. Coniglio
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  4. Abilio Rodrigues Filho
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Corresponding author

Correspondence to Juliana Bueno-Soler .

Editor information

Editors and Affiliations

  1. Department of Humanities, University of Pavia, Piazza Botta 6, 27100, Pavia, Italy

    Lorenzo Magnani  & Tommaso Bertolotti  & 

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Bueno-Soler, J., Carnielli, W., Coniglio, M.E., Rodrigues Filho, A. (2017). Formal (In)consistency, Abduction and Modalities. In: Magnani, L., Bertolotti, T. (eds) Springer Handbook of Model-Based Science. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-30526-4_15

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  • DOI: https://doi.org/10.1007/978-3-319-30526-4_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30525-7

  • Online ISBN: 978-3-319-30526-4

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