An alternative rule of disjunction in modal logic

Notre Dame Journal of Formal Logic 33 (1):89-100 (1991)
  Copy   BIBTEX

Abstract

Lemmon and Scott introduced the notion of a modal system's providing the rule of disjunction. No consistent normal extension of KB provides this rule. An alternative rule is defined, which KDB, KTB, and other systems are shown to provide, while K and other systems provide the Lemmon-Scott rule but not the alternative rule. If S provides the alternative rule then either —A is a theorem of S or A is whenever A -> ΠA is a theorem; the converse fails. It is suggested that systems with this property are appropriate for handling sorites paradoxes, where D is read as 'clearly*. The S4 axiom fails in such systems

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 102,546

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

Normal derivability in modal logic.Jan von Plato - 2005 - Mathematical Logic Quarterly 51 (6):632-638.
Canonical Rules.Emil Jeřábek - 2009 - Journal of Symbolic Logic 74 (4):1171 - 1205.
A rule-completeness theorem.Nuel D. Belnap & Richmond H. Thomason - 1963 - Notre Dame Journal of Formal Logic 4 (1):39-43.
Locality for Classical Logic.Kai Brünnler - 2006 - Notre Dame Journal of Formal Logic 47 (4):557-580.

Analytics

Added to PP
2010-08-24

Downloads
58 (#379,014)

6 months
23 (#131,342)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Timothy Williamson
University of Oxford

Citations of this work

Supervaluationism, Modal Logic, and Weakly Classical Logic.Joshua Schechter - 2024 - Journal of Philosophical Logic 53 (2):411-61.
Explicating Logical Independence.Lloyd Humberstone - 2020 - Journal of Philosophical Logic 49 (1):135-218.
Inexact Knowledge with Introspection.Denis Bonnay & Paul Égré - 2009 - Journal of Philosophical Logic 38 (2):179-227.
On Rules.Rosalie Iemhoff - 2015 - Journal of Philosophical Logic 44 (6):697-711.
Modal logics with the MacIntosh rule.Brian F. Chellas & Krister Segerberg - 1994 - Journal of Philosophical Logic 23 (1):67 - 86.

View all 10 citations / Add more citations

References found in this work

No references found.

Add more references