The Power of a Propositional Constant

Journal of Philosophical Logic (1):1-20 (2012)
  Copy   BIBTEX


Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of extensions of S4.3 is radically altered by the addition of a constant: we use it to construct continuum many such normal extensions of S4.3, and continuum many non-normal ones, none of which have the finite model property. But for logics with weakly transitive frames there are only eight maximally normal ones, of which five extend K4 and three extend S4



    Upload a copy of this work     Papers currently archived: 91,322

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

Incompleteness and the Barcan formula.M. J. Cresswell - 1995 - Journal of Philosophical Logic 24 (4):379 - 403.
Normal monomodal logics can simulate all others.Marcus Kracht & Frank Wolter - 1999 - Journal of Symbolic Logic 64 (1):99-138.
Modal incompleteness revisited.Tadeusz Litak - 2004 - Studia Logica 76 (3):329 - 342.
Interpretations of intuitionist logic in non-normal modal logics.Colin Oakes - 1999 - Journal of Philosophical Logic 28 (1):47-60.
An ideal characterization of mahlo cardinals.Qi Feng - 1989 - Journal of Symbolic Logic 54 (2):467-473.
Infinitary propositional normal modal logic.Slavian Radev - 1987 - Studia Logica 46 (4):291 - 309.


Added to PP

53 (#293,652)

6 months
6 (#522,885)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Tomasz Kowalski
La Trobe University

Citations of this work

A Logic of Temporal Contingency.Jie Fan - forthcoming - Erkenntnis:1-30.
Note on Extending Congruential Modal Logics.Lloyd Humberstone - 2016 - Notre Dame Journal of Formal Logic 57 (1):95-103.
Post Completeness in Congruential Modal Logics.Peter Fritz - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. College Publications. pp. 288-301.
An observation concerning porte's rule in modal logic.Rohan French & Lloyd Humberstone - 2015 - Bulletin of the Section of Logic 44 (1/2):25-31.
A Note on the Issue of Cohesiveness in Canonical Models.Matteo Pascucci - 2020 - Journal of Logic, Language and Information 29 (3):331-348.

View all 6 citations / Add more citations

References found in this work

An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
From Frege to Gödel.Jean Van Heijenoort (ed.) - 1967 - Cambridge,: Harvard University Press.
Modal logic.Alexander Chagrov - 1997 - New York: Oxford University Press. Edited by Michael Zakharyaschev.
Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.
Dynamic Logic.Lenore D. Zuck & David Harel - 1989 - Journal of Symbolic Logic 54 (4):1480.

View all 29 references / Add more references