Limits for Paraconsistent Calculi

Notre Dame Journal of Formal Logic 40 (3):375-390 (1999)
  Copy   BIBTEX

Abstract

This paper discusses how to define logics as deductive limits of sequences of other logics. The case of da Costa's hierarchy of increasingly weaker paraconsistent calculi, known as $ \mathcal {C}$n, 1 $ \leq$ n $ \leq$ $ \omega$, is carefully studied. The calculus $ \mathcal {C}$$\scriptstyle \omega$, in particular, constitutes no more than a lower deductive bound to this hierarchy and differs considerably from its companions. A long standing problem in the literature (open for more than 35 years) is to define the deductive limit to this hierarchy, that is, its greatest lower deductive bound. The calculus $ \mathcal {C}$min, stronger than $ \mathcal {C}$$\scriptstyle \omega$, is first presented as a step toward this limit. As an alternative to the bivaluation semantics of $ \mathcal {C}$min presented thereupon, possible-translations semantics are then introduced and suggested as the standard technique both to give this calculus a more reasonable semantics and to derive some interesting properties about it. Possible-translations semantics are then used to provide both a semantics and a decision procedure for $ \mathcal {C}$Lim, the real deductive limit of da Costa's hierarchy. Possible-translations semantics also make it possible to characterize a precise sense of duality: as an example, $ \mathcal {D}$min is proposed as the dual to $ \mathcal {C}$min.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,140

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Classical Modal De Morgan Algebras.Sergio A. Celani - 2011 - Studia Logica 98 (1-2):251-266.
Semi-intuitionistic Logic.Juan Manuel Cornejo - 2011 - Studia Logica 98 (1-2):9-25.
On Partial and Paraconsistent Logics.Reinhard Muskens - 1999 - Notre Dame Journal of Formal Logic 40 (3):352-374.
Ideal Paraconsistent Logics.O. Arieli, A. Avron & A. Zamansky - 2011 - Studia Logica 99 (1-3):31-60.
Yes, Virginia, there really are paraconsistent logics.Bryson Brown - 1999 - Journal of Philosophical Logic 28 (5):489-500.

Analytics

Added to PP
2010-08-24

Downloads
50 (#236,391)

6 months
1 (#447,993)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Joao Marcos
Universidade Federal do Rio Grande do Norte
Walter Carnielli
University of Campinas

Citations of this work

Paraconsistent Logic.David Ripley - 2015 - Journal of Philosophical Logic 44 (6):771-780.

View all 18 citations / Add more citations

References found in this work

On the Theory of Inconsistent Formal Systems.Newton C. A. Costa - 1972 - Recife, Universidade Federal De Pernambuco, Instituto De Matemática.
On the theory of inconsistent formal systems.Newton C. A. da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.

View all 13 references / Add more references