The Power of a Propositional Constant


Authors
Tomasz Kowalski
La Trobe University
Abstract
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
Keywords Propositional constant  Maximally normal modal logic  Post complete  Kripke-incomplete  Anti-complete  Weakly transitive
Categories (categorize this paper)
DOI 10.1007/s10992-012-9256-0
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 45,662
Through your library

References found in this work BETA

Modal Logic.Alexander Chagrov - 1997 - Oxford University Press.
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.
Semantic Analysis of Tense Logics.S. K. Thomason - 1972 - Journal of Symbolic Logic 37 (1):150-158.

View all 25 references / Add more references

Citations of this work BETA

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.

Add more citations

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.

Analytics

Added to PP index
2012-12-15

Total views
37 ( #240,960 of 2,280,725 )

Recent downloads (6 months)
5 ( #245,716 of 2,280,725 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature