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) |
|---|---|
| Title of host publication | Philosophy of Logic |
| Publisher | Elsevier |
| Pages | 791-911 |
| Number of pages | 121 |
| ISBN (Print) | 9780444515414 |
| DOIs | |
| State | Published - 2007 |
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ASJC Scopus subject areas
- Mathematics(all)
Cite this
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 proceeding › Chapter
}
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.
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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 -