Authors
José M. Méndez
Universidad de Salamanca
Gemma Robles
Universidad de León
Abstract
In a standard sense, consistency and paraconsistency are understood as the absence of any contradiction and as the absence of the ECQ (‘E contradictione quodlibet’) rule, respectively. The concepts of weak consistency (in two different senses) as well as that of F -consistency have been defined by the authors. The aim of this paper is (a) to define alternative (to the standard one) concepts of paraconsistency in respect of the aforementioned notions of weak consistency and F -consistency; (b) to define the concept of strong paraconsistency; (c) to build up a series of strongly paraconsistent logics; (d) to define the basic constructive logic adequate to a rather weak sense of consistency. All logics treated in this paper are strongly paraconsistent. All of them are sound and complete in respect a modification of Routley and Meyer’s ternary relational semantics for relevant logics (no logic in this paper is relevant).
Keywords Consistency  Paraconsistent logics  Constructive negation  Substructural logics  Ternary relational semantics
Categories (categorize this paper)
DOI 10.1007/s10849-009-9085-x
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 58,425
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Paraconsistent Logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
A Propositional Calculus with Denumerable Matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Negation in Relevant Logics (How I Stopped Worrying and Learned to Love the Routley Star).Greg Restall - 1999 - In Dov M. Gabbay & Heinrich Wansing (eds.), What is Negation? Kluwer Academic Publishers. pp. 53-76.

View all 16 references / Add more references

Citations of this work BETA

Paraconsistent Logics Included in Lewis’ S4.Gemma Robles & José M. Méndez - 2010 - Review of Symbolic Logic 3 (3):442-466.

Add more citations

Similar books and articles

The Basic Constructive Logic for Negation-Consistency.Gemma Robles - 2008 - Journal of Logic, Language and Information 17 (2):161-181.
The Basic Constructive Logic for Absolute Consistency.José M. Méndez & Gemma Robles - 2009 - Journal of Logic, Language and Information 18 (2):199-216.
Logic and the Consistency of the World.Joseph Wayne Smith - 1986 - Erkenntnis 24 (2):105 - 114.
Paraconsistent Logics Included in Lewis’ S4.Gemma Robles & José M. Méndez - 2010 - Review of Symbolic Logic 3 (3):442-466.
The Consistency Strength of an Infinitary Ramsey Property.George Kafkoulis - 1994 - Journal of Symbolic Logic 59 (4):1158-1195.
The Basic Constructive Logic for a Weak Sense of Consistency.Gemma Robles & José M. Méndez - 2008 - Journal of Logic, Language and Information 17 (1):89-107.

Analytics

Added to PP index
2009-03-09

Total views
45 ( #226,485 of 2,420,820 )

Recent downloads (6 months)
1 ( #543,487 of 2,420,820 )

How can I increase my downloads?

Downloads

My notes