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Logics of formal inconsistency. (English) Zbl 1266.03006
Gabbay, Dov M. (ed.) et al., Handbook of philosophical logic. Vol. 14. Dordrecht: Springer (ISBN 978-90-481-7608-3/pbk; 978-1-4020-6323-7/hbk; 978-1-4020-6324-4/ebook). Handbook of Philosophical Logic 14, 1-93 (2007).
From the text: In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory entails all possible consequences) are assumed inseparable, granted that negation is available. This is an effect of an ordinary logical feature known as ‘explosiveness’: According to it, from a contradiction ‘\(\alpha\) and \(\neg\alpha\)’ everything is derivable. Indeed, classical logic (and many other logics) equate ‘consistency’ with ‘freedom from contradictions’. Such logics forcibly fail to distinguish, thus, between contradictoriness and other forms of inconsistency. Paraconsistent logics are precisely the logics for which this assumption is challenged, by the rejection of the classical ‘consistency presupposition’.
For a review of the entire collection see [Zbl 1259.03001].
For the entire collection see [Zbl 1259.03001].

MSC:
03A05 Philosophical and critical aspects of logic and foundations
03B53 Paraconsistent logics
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