Collapsing Modalities
Lloyd Humberstone
Source: Notre Dame J. Formal Logic Volume 50, Number 2
(2009), 119-132.
Abstract
Sections 1 and 2 respectively raise and settle the question of whether, if an affirmative modality collapses (reduces to the null modality, that is) in a normal modal logic, then all modalities of the same length collapse in that logic, while Section 3 considers some special cases of an analogous phenomenon for congruential modal logics, closing with a general question about collapsing modalities in this broader range of logics.
First Page:
Show
Hide
Primary Subjects:
03B45
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1242067705
Digital Object Identifier: doi:10.1215/00294527-2009-001
Mathematical Reviews number (MathSciNet): MR2535579
Zentralblatt MATH identifier: 05635605
References
[1] Bellissima, F., and M. Mirolli, "A general treatment of equivalent modalities", The Journal of Symbolic Logic, vol. 54 (1989), pp. 1460--71.
Mathematical Reviews (MathSciNet): MR1026610
Zentralblatt MATH: 0706.03017
Digital Object Identifier: doi:10.2307/2274826
JSTOR: links.jstor.org
[2] van Benthem, J. F. A. K., "Modal reduction principles", The Journal of Symbolic Logic, vol. 41 (1976), pp. 301--12.
Mathematical Reviews (MathSciNet): MR0409111
Zentralblatt MATH: 0337.02014
Digital Object Identifier: doi:10.2307/2272228
JSTOR: links.jstor.org
[3] Chellas, B., "Modalities in normal systems containing the S5 axiom", pp. 261--65 in Intention and Intentionality: Essays in Honour of G. E. M. Anscombe, edited by C. Diamond and J. Teichman, Harvester Press, Brighton, 1979.
[4] Chellas, B. F., Modal Logic. An Introduction, Cambridge University Press, Cambridge, 1980.
Mathematical Reviews (MathSciNet): MR556867
Zentralblatt MATH: 0431.03009
[5] Fitch, F. B., "A correlation between modal reduction principles and properties of relations", Journal of Philosophical Logic, vol. 2 (1973), pp. 97--101.
Mathematical Reviews (MathSciNet): MR0414319
Zentralblatt MATH: 0259.02012
Digital Object Identifier: doi:10.1007/BF02115611
[6] Giesl, J., and D. Kapur, "Dependency pairs for equational rewriting", pp. 93--107 in Rewriting Techniques and Applications (Utrecht, 2001), edited by A. Middeldorp, vol. 2051 of Lecture Notes in Computer Science, Springer, Berlin, 2001.
Mathematical Reviews (MathSciNet): MR1892391
Zentralblatt MATH: 0981.68063
Digital Object Identifier: doi:10.1007/3-540-45127-7_9
[7] Humberstone, L., "Negation by iteration", Theoria, vol. 61 (1995), pp. 1--24.
Mathematical Reviews (MathSciNet): MR1619613
Zentralblatt MATH: 0883.03007
[8] Humberstone, L., "Two-dimensional adventures", Philosophical Studies, vol. 118 (2004), pp. 17--65.
Mathematical Reviews (MathSciNet): MR2068363
Digital Object Identifier: doi:10.1023/B:PHIL.0000019542.43440.d1
[9] Humberstone, L., and T. Williamson, "Inverses for normal modal operators", Studia Logica, vol. 59 (1997), pp. 33--64.
Mathematical Reviews (MathSciNet): MR1470208
Zentralblatt MATH: 0887.03015
Digital Object Identifier: doi:10.1023/A:1004995316790
[10] Parry, W. T., "Modalities in the survey" system of strict implication, The Journal of Symbolic Logic, vol. 4 (1939), pp. 137--54.
Mathematical Reviews (MathSciNet): MR0000809
Zentralblatt MATH: 0023.09902
Digital Object Identifier: doi:10.2307/2268714
[11] Williamson, T., "Two incomplete anti-realist modal epistemic logics", The Journal of Symbolic Logic, vol. 55 (1990), pp. 297--314.
Mathematical Reviews (MathSciNet): MR1043559
Zentralblatt MATH: 0706.03019
Digital Object Identifier: doi:10.2307/2274969
JSTOR: links.jstor.org
[12] Williamson, T., "Continuum many maximal consistent normal bimodal logics with inverses", Notre Dame Journal of Formal Logic, vol. 39 (1998), pp. 128--34.
Mathematical Reviews (MathSciNet): MR1671746
Zentralblatt MATH: 0968.03027
Digital Object Identifier: doi:10.1305/ndjfl/1039293024
Project Euclid: euclid.ndjfl/1039293024
Notre Dame Journal of Formal Logic
