An infinity of super-Belnap logics

Journal of Applied Non-Classical Logics 22 (4):319 - 335 (2012)
  Copy   BIBTEX

Abstract

We look at extensions (i.e., stronger logics in the same language) of the Belnap?Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap?Dunn and do not coincide with any of the known extensions (Kleene?s logics, Priest?s logic of paradox). We characterise the reduced algebraic models of these new logics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite logical matrix. We show that the last logic of the chain is not finitely axiomatisable

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,346

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

On Partial and Paraconsistent Logics.Reinhard Muskens - 1999 - Notre Dame Journal of Formal Logic 40 (3):352-374.
Partiality and its dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.
Hybrid logics of separation axioms.Dmitry Sustretov - 2009 - Journal of Logic, Language and Information 18 (4):541-558.

Analytics

Added to PP
2013-03-01

Downloads
26 (#449,240)

6 months
1 (#450,993)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Introduction to Metamathematics.Stephen Cole Kleene - 1952 - Princeton, NJ, USA: North Holland.
An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Amsterdam, Netherlands: Warszawa, Pwn - Polish Scientific Publishers.
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.
Theory of Logical Calculi: Basic Theory of Consequence Operations.Ryszard Wójcicki - 1988 - Dordrecht, Boston and London: Kluwer Academic Publishers.

View all 23 references / Add more references