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.
Keywords
- Consistent Performance
- Paraconsistent Negation
- Consistency Propagation
- Inconsistent Performance
- Possible-translations Semantics
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes
- 1.
In general, names of logic systems are acronyms for the names of the axioms involved.
- 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.
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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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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