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Some Extensions of mbC

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Paraconsistent Logic: Consistency, Contradiction and Negation

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 40))

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Abstract

This chapter deals with several extensions of mbC, which by its turn is a minimal extension of positive classical logic by means of a consistency operator and a paraconsistent negation. Important topics studied are consistency and inconsistency as derived connectives, inconsistency operators, as well as N. da Costa’s Hierarchy and consistency propagation.

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Notes

  1. 1.

    In general, names of logic systems are acronyms for the names of the axioms involved.

  2. 2.

    As it was done above, to simplify notation, the index \(\beta \) will kept fixed in the statement and in the proof of this proposition. Of course this abuse of notation does not affect the validity of the claims, because of the properties of \(\bot _{\beta (\alpha )}\), \({\sim }_{\beta (\alpha )}\) and \({\circ }_{\beta (\alpha )}\).

  3. 3.

    As a concrete example of this situation, consider the expansion \(C_2^{\sim }\) of da Costa’s system \(C_2\) (see Sect. 3.7) obtained by adding a primitive connective for the classical negation \({\sim }\), where \({\circ }_1 p\) and \({\circ }_2 p\) are formulas which only use \(\wedge \) and \(\lnot \), and where the formula \(\psi (p_1,p_2)\) is \({\sim }(p_1 \rightarrow \sim p_2)\).

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Authors and Affiliations

  1. Department of Philosophy and Centre for Logic, Epistemology and the History of Science (CLE), University of Campinas (UNICAMP), Campinas, São Paulo, Brazil

    Walter Carnielli & Marcelo Esteban Coniglio

Authors
  1. Walter Carnielli
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  2. Marcelo Esteban Coniglio
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Correspondence to Walter Carnielli .

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Carnielli, W., Coniglio, M.E. (2016). Some Extensions of mbC. In: Paraconsistent Logic: Consistency, Contradiction and Negation. Logic, Epistemology, and the Unity of Science, vol 40. Springer, Cham. https://doi.org/10.1007/978-3-319-33205-5_3

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