Nelson's negation on the base of weaker versions of intuitionistic negation

Studia Logica 80 (2-3):393 - 430 (2005)
Constructive logic with <span class='Hi'>Nelson</span> negation is an extension of the intuitionistic logic with a special type of negation expressing some features of constructive falsity and refutation by counterexample. In this paper we generalize this logic weakening maximally the underlying intuitionistic negation. The resulting system, called subminimal logic with <span class='Hi'>Nelson</span> negation, is studied by means of a kind of algebras called generalized N-lattices. We show that generalized N-lattices admit representation formalizing the intuitive idea of refutation by means of counterexamples giving in this way a counterexample semantics of the logic in question and some of its natural extensions. Among the extensions which are near to the intuitionistic logic are the minimal logic with <span class='Hi'>Nelson</span> negation which is an extension of the Johansson's minimal logic with <span class='Hi'>Nelson</span> negation and its in a sense dual version — the co-minimal logic with <span class='Hi'>Nelson</span> negation. Among the extensions near to the classical logic are the well known 3-valued logic of Lukasiewicz, two 12-valued logics and one 48-valued logic. Standard questions for all these logics — decidability, Kripke-style semantics, complete axiomatizability, conservativeness are studied. At the end of the paper extensions based on a new connective of self-dual conjunction and an analog of the Lukasiewicz middle value ½ have also been considered.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
Categories (categorize this paper)
DOI 10.2307/20016723
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 16,667
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
Ofer Arieli & Arnon Avron (1996). Reasoning with Logical Bilattices. Journal of Logic, Language and Information 5 (1):25--63.

View all 17 references / Add more references

Citations of this work BETA
Heinrich Wansing (2008). Constructive Negation, Implication, and Co-Implication. Journal of Applied Non-Classical Logics 18 (2-3):341-364.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

16 ( #167,478 of 1,726,249 )

Recent downloads (6 months)

3 ( #231,316 of 1,726,249 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.