By Walter Carnielli, Marcelo Esteban Coniglio

This ebook is the 1st within the box of paraconsistency to provide a accomplished review of the topic, together with connections to different logics and purposes in info processing, linguistics, reasoning and argumentation, and philosophy of technological know-how. it is suggested examining for an individual attracted to the query of reasoning and argumentation within the presence of contradictions, in semantics, within the paradoxes of set idea and within the difficult houses of negation in good judgment programming. Paraconsistent good judgment contains an enormous logical conception and provides the broadest attainable viewpoint at the debate of negation in good judgment and philosophy. it's a strong software for reasoning less than contradictoriness because it investigates common sense platforms within which contradictory info doesn't result in arbitrary conclusions. Reasoning less than contradictions constitutes one in all most vital and artistic achievements in modern good judgment, with deep roots in philosophical questions regarding negation and consistency

This publication bargains a useful advent to a subject of significant value in good judgment and philosophy. It discusses (i) the heritage of paraconsistent common sense; (ii) language, negation, contradiction, consistency and inconsistency; (iii) logics of formal inconsistency (LFIs) and the most paraconsistent propositional platforms; (iv) many-valued partners, possible-translations semantics and non-deterministic semantics; (v) paraconsistent modal logics; (vi) first-order paraconsistent logics; (vii) functions to info processing, databases and quantum computation; and (viii) functions to deontic paradoxes, connections to jap inspiration and to dialogical reasoning.

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Extra resources for Paraconsistent Logic: Consistency, Contradiction and Negation

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A. da Costa (see [12]) presented his famous hierarchy of paraconsistent systems Cn (for n ≥ 1), constituting the broadest formal study of paraconsistency proposed up to that time. It is worth mentioning here what has been said by da Costa, in private conversation: “As with the discovery of America, many people are said to have discovered paraconsistent logic before my work. ” The Argentinian philosopher F. Asenjo introduced, in 1966 (see [21]), a threevalued logic as a formal framework for studying antinomies.

For now, we want to emphasize that the sketch of a paraconsistent logic in which contradictions are epistemologically understood as conflicting evidence, and not as a pair of contradictory true sentences, is inspired by an analysis of real situations of reasoning in which contradictions occur. The notion of evidence is weaker than truth in the sense that, if we know that α is true, then there must be some evidence for α, but the fact that there is evidence for α does not imply that α is true. A paraconsistent logic may thus be obtained analogously to the way intuitionistic logic has been obtained.

A violation of PNC-O would be an object a and a property P such that a has and does not have P. Hence, in order to show that PNC-O is true, one needs to show that there can be no such object. This problem may be naturally divided into two parts, one related to mathematics, the other related to empirical sciences. With respect to the former, a proof of PNC-O would be tantamount to showing that mathematics is consistent. But this cannot be proven, even with respect to arithmetic. With respect to the latter, there is an extensive literature about the occurrence of contradictions in empirical theories (see, for example, Chap.

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