Logique Et Analyse 48 (189-192):279-300 (2005)

Joao Marcos
Universidade Federal do Rio Grande do Norte
An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its negation are satisfied. Paraconsistent logics are negation-inconsistent yet non-overcomplete; paracomplete logics are negation-incomplete yet non-overcomplete. A paranormal logic is simply a logic that is both paraconsistent and paracomplete. Despite being perfectly consistent and complete with respect to classical negation, nearly every normal modal logic, in its ordinary language and interpretation, admits to some latent paranormality: It is paracomplete with respect to a negation defined as an impossibility operator, and paraconsistent with respect to a negation defined as non-necessity. In fact, as it will be shown here, even in languages without a primitive classical negation, normal modal logics can often be alternatively characterized directly by way of their paranormal negations and related operators. So, instead of talking about ‘necessity’, ‘possibility’, and so on, modal logics could be seen just as devices tailored for the study of (modal) negation. This paper shows how and to what extent this alternative characterization of modal logics can be realized.
Keywords paraconsistent logic  paracomplete logic  modal logic
Categories (categorize this paper)
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: 55,981
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

Modal Logic: An Introduction.Brian F. Chellas - 1980 - Cambridge University Press.
A Natural History of Negation.Laurence Horn - 1989 - University of Chicago Press.
A Natural History of Negation.Jon Barwise & Laurence R. Horn - 1991 - Journal of Symbolic Logic 56 (3):1103.
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 19 references / Add more references

Citations of this work BETA

Defining LFIs and LFUs in Extensions of Infectious Logics.Szmuc Damian Enrique - 2016 - Journal of Applied Non-Classical Logics 26 (4):286-314.

View all 23 citations / Add more citations

Similar books and articles

Interpretations of Intuitionist Logic in Non-Normal Modal Logics.Colin Oakes - 1999 - Journal of Philosophical Logic 28 (1):47-60.
Normal Monomodal Logics Can Simulate All Others.Marcus Kracht & Frank Wolter - 1999 - Journal of Symbolic Logic 64 (1):99-138.
Infinitary Propositional Normal Modal Logic.Slavian Radev - 1987 - Studia Logica 46 (4):291 - 309.
A Splitting Logic in NExt(KTB).Yutaka Miyazaki - 2007 - Studia Logica 85 (3):381 - 394.
Logics of Essence and Accident.Joao Marcos - 2005 - Bulletin of the Section of Logic 34 (1):43-56.
Is Normal Memory a Paranormal Phenomenon?John Beloff - 1980 - Theoria to Theory 14 (September):145-162.


Added to PP index

Total views
34 ( #299,409 of 2,403,482 )

Recent downloads (6 months)
2 ( #360,890 of 2,403,482 )

How can I increase my downloads?


My notes