Paraconsistent Logics and Paraconsistency

Newton C.A. da Costa, Décio A. Krause, Otávio A. Bueno

Research output: Chapter in Book/Report/Conference proceedingChapter

35 Scopus citations

Abstract

This chapter discusses paraconsistent logics (PL) and paraconsistency. PL are the logics of inconsistent but nontrivial theories. A deductive theory is paraconsistent if its underlying logic is paraconsistent. A theory is inconsistent if there is a formula (a grammatically well-formed expression of its language) such that the formula and its negation are both theorems of the theory; otherwise, the theory is called consistent. A theory is trivial if all formulas of its language are theorems. In a trivial theory "everything" (expressed in its language) can be proved. If the underlying logic of a theory is classical logic, or even any of the standard logical systems such as intuitionistic logic, inconsistency entails triviality, and conversely. This chapter discusses da Costa's C-logics. This chapter elaborates on paraconsistent set theories, and shows, in particular, how they accommodate inconsistent objects, such as the Russell set. Jáskowski's discussive logic is examined, and it is showed how it can be used in the formulation of the concept of partial truth. The chapter also examines annotated logic, and some of its applications.

Original languageEnglish (US)
Title of host publicationPhilosophy of Logic
PublisherElsevier
Pages791-911
Number of pages121
ISBN (Print)9780444515414
DOIs
StatePublished - Dec 1 2007

ASJC Scopus subject areas

  • Mathematics(all)

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    da Costa, N. C. A., Krause, D. A., & Bueno, O. A. (2007). Paraconsistent Logics and Paraconsistency. In Philosophy of Logic (pp. 791-911). Elsevier. https://doi.org/10.1016/B978-044451541-4/50023-3