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Contradictions, from consistency to inconsistency. (English) Zbl 1419.03004
Trends in Logic – Studia Logica Library 47. Cham: Springer (ISBN 978-3-319-98796-5/hbk; 978-3-319-98797-2/ebook). vi, 322 p. (2018).

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Publisher’s description: This volume investigates what is beyond the Principle of Non-Contradiction. It features 14 papers on the foundations of reasoning, including logical systems and philosophical considerations. Coverage brings together a cluster of issues centered upon the variety of meanings of consistency, contradiction, and related notions.
Most of the papers, but not all, are developed around the subtle distinctions between consistency and non-contradiction, as well as among contradiction, inconsistency, and triviality, and concern one of the above mentioned threads of the broadly understood non-contradiction principle and the related principle of explosion. Some others take a perspective that is not too far away from such themes, but with the freedom to tread new paths.
Readers should understand the title of this book in a broad way, because it is not so obvious to deal with notions like contradictions, consistency, inconsistency, and triviality. The papers collected here present groundbreaking ideas related to consistency and inconsistency.
The articles of this volume will be reviewed individually.
Indexed articles:
Arenhart, Jonas R. Becker, The price of true contradictions about the world, 11-31 [Zbl 1439.03028]
Estrada-González, Luis; Martínez-Ordaz, María del Rosario, The possibility and fruitfulness of a debate on the principle of non-contradiction, 33-51 [Zbl 1439.03017]
Friend, Michèle; Martínez-Ordaz, María del Rosario, Keeping globally inconsistent scientific theories locally consistent, 53-88 [Zbl 1439.03029]
Barrio, Eduardo; Pailos, Federico; Szmuc, Damian, What is a paraconsistent logic?, 89-108 [Zbl 1439.03062]
Gaytán, David; D’Ottaviano, Itala M. Loffredo; Morado, Raymundo, Provided you’re not trivial: adding defaults and paraconsistency to a formal model of explanation, 109-138 [Zbl 1439.03063]
Woltzenlogel Paleo, Bruno, Para-disagreement logics and their implementation through embedding in Coq and SMT, 139-158 [Zbl 1439.03066]
Džamonja, Mirna; Panza, Marco, Asymptotic quasi-completeness and ZFC, 159-182 [Zbl 1439.03085]
Freire, Rodrigo A., Interpretation and truth in set theory, 183-205 [Zbl 1439.03020]
Mundici, Daniele, Coherence of the product law for independent continuous events, 207-212 [Zbl 1439.06009]
Rioul, Olivier; Magossi, José Carlos, A local-global principle for the real continuum, 213-240 [Zbl 1439.26014]
Finger, Marcelo, Quantitative logic reasoning, 241-271 [Zbl 1439.03059]
Carnielli, Walter; Mariano, Hugo Luiz; Matulovic, Mariana, Reconciling first-order logic to algebra, 273-305 [Zbl 1439.03109]
Marcelino, Sérgio; Caleiro, Carlos; Rivieccio, Umberto, Plug and play negations, 307-322 [Zbl 1439.03064]

MSC:
03-06 Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations
03A05 Philosophical and critical aspects of logic and foundations
03B53 Paraconsistent logics
03E35 Consistency and independence results
00B15 Collections of articles of miscellaneous specific interest
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