# Paraconsistent Logics and Paraconsistency

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

Research output: Chapter in Book/Report/Conference proceedingChapter

33 Citations (Scopus)

### 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 language English (US) Philosophy of Logic Elsevier 791-911 121 9780444515414 https://doi.org/10.1016/B978-044451541-4/50023-3 Published - 2007

### Fingerprint

Paraconsistent Logic
Logic
Inconsistent
Trivial
Intuitionistic Logic
Classical Logic
Set Theory
Theorem
Inconsistency
Partial
Formulation

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

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

Paraconsistent Logics and Paraconsistency. / da Costa, Newton C A; Krause, Décio A.; Bueno, Otavio.

Philosophy of Logic. Elsevier, 2007. p. 791-911.

Research output: Chapter in Book/Report/Conference proceedingChapter

da Costa, NCA, Krause, DA & Bueno, O 2007, Paraconsistent Logics and Paraconsistency. in Philosophy of Logic. Elsevier, pp. 791-911. https://doi.org/10.1016/B978-044451541-4/50023-3
da Costa NCA, Krause DA, Bueno O. Paraconsistent Logics and Paraconsistency. In Philosophy of Logic. Elsevier. 2007. p. 791-911 https://doi.org/10.1016/B978-044451541-4/50023-3
da Costa, Newton C A ; Krause, Décio A. ; Bueno, Otavio. / Paraconsistent Logics and Paraconsistency. Philosophy of Logic. Elsevier, 2007. pp. 791-911
@inbook{b5928349f0854c45a1cee4e01b137906,
title = "Paraconsistent Logics and Paraconsistency",
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. J{\'a}skowski'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.",
author = "{da Costa}, {Newton C A} and Krause, {D{\'e}cio A.} and Otavio Bueno",
year = "2007",
doi = "10.1016/B978-044451541-4/50023-3",
language = "English (US)",
isbn = "9780444515414",
pages = "791--911",
booktitle = "Philosophy of Logic",
publisher = "Elsevier",

}

TY - CHAP

T1 - Paraconsistent Logics and Paraconsistency

AU - da Costa, Newton C A

AU - Krause, Décio A.

AU - Bueno, Otavio

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38549167547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38549167547&partnerID=8YFLogxK

U2 - 10.1016/B978-044451541-4/50023-3

DO - 10.1016/B978-044451541-4/50023-3

M3 - Chapter

AN - SCOPUS:38549167547

SN - 9780444515414

SP - 791

EP - 911

BT - Philosophy of Logic

PB - Elsevier

ER -