Normality operators and classical recapture in many-valued logic

Logic Journal of the IGPL 28 (5):657-683 (2020)
  Copy   BIBTEX


In this paper, we use a ‘normality operator’ in order to generate logics of formal inconsistency and logics of formal undeterminedness from any subclassical many-valued logic that enjoys a truth-functional semantics. Normality operators express, in any many-valued logic, that a given formula has a classical truth value. In the first part of the paper we provide some setup and focus on many-valued logics that satisfy some of the three properties, namely subclassicality and two properties that we call fixed-point negation property and conservativeness. In the second part of the paper, we introduce normality operators and explore their formal behaviour. In the third and final part of the paper, we establish a number of classical recapture results for systems of formal inconsistency and formal undeterminedness that satisfy some or all the properties above. These are the main formal results of the paper. Also, we illustrate concrete cases of recapture by discussing the logics $\mathsf{K}^{\circledast }_{3}$, $\mathsf{LP}^{\circledast }$, $\mathsf{K}^{w\circledast }_{3}$, $\mathsf{PWK}^{\circledast }$ and $\mathsf{E_{fde}}^{\circledast }$, that are in turn extensions of $\mathsf{{K}_{3}}$, $\mathsf{LP}$, $\mathsf{K}^{w}_{3}$, $\mathsf{PWK}$ and $\mathsf{E_{fde}}$, respectively.



    Upload a copy of this work     Papers currently archived: 74,509

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

Normality Operators and Classical Collapse.Roberto Ciuni & Massimiliano Carrara - 2018 - In T. Arazim P. And Lavicka (ed.), The Logica Yearbook 2017. Londra, Regno Unito: pp. 2-20.
How to Avoid Deviance (in Logic).Walter Sinnott-Armstrong & Amit Malhotra - 2002 - History and Philosophy of Logic 23 (3):215--36.
The Operators of Vector Logic.Eduardo Mizraji - 1996 - Mathematical Logic Quarterly 42 (1):27-40.
Some Operators in Kripke Models with an Involution.A. Galli & M. Sagastume - 1999 - Journal of Applied Non-Classical Logics 9 (1):107-120.
A Robust Non-Transitive Logic.Alan Weir - 2015 - Topoi 34 (1):1-9.
Term-Forming Operators in First Order Logic.David Michael Devidi - 1994 - Dissertation, The University of Western Ontario (Canada)
Mixed Logic and Storage Operators.Karim Nour - 2000 - Archive for Mathematical Logic 39 (4):261-280.
Tensed Ontology Based on Simple Partial Logic.Daisuke Kachi - 2002 - Proceedings of Ninth International Symposium on Temporal Representation and Reasoning: TIME-02:141-145.


Added to PP

14 (#725,396)

6 months
1 (#417,896)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Massimiliano Carrara
University of Padua

Citations of this work

Semantical Analysis of Weak Kleene Logics.Roberto Ciuni & Massimiliano Carrara - 2019 - Journal of Applied Non-Classical Logics 29 (1):1-36.

Add more citations

References found in this work

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
On the Theory of Inconsistent Formal Systems.Newton C. A. Costa - 1972 - Recife, Universidade Federal De Pernambuco, Instituto De Matemática.

View all 31 references / Add more references