Journal of Applied Non-Classical Logics 17 (4):521-543 (2007)
Abstract |
This is primarily a conceptual paper. The goal of the paper is to put into perspective the proof-theory of hybrid logic and in particular, try to give an answer to the following question: Why does the proof-theory of hybrid logic work so well compared to the proof-theory of ordinary modal logic? Roughly, there are two different kinds of proof systems for modal logic: Systems where the formulas involved in the rules are formulas of the object language, that is, ordinary modal-logical formulas, and systems where the formulas involved in the rules are metalingustic formulas obtained by attaching labels representing possible worlds to ordinary modal-logical formulas. Systems of the second kind often also involve an explicit representation of the accessibility relation. From a proof-theoretic point of view, modal-logical systems of the first kind are less well-behaved than systems of the second kind. It turns out that this can be remedied by hybridization, that is, hybridization of modal logics enables the formulation of well-behaved proof systems without involving metalinguistic machinery. What has happened is that the metalinguistic machinery has been internalized in the object language. This gives an answer to the initial question, which is that the proof-theory of hybrid logic works so well because the metalinguistic semantic machinery has been internalized in the object language.
|
Keywords | No keywords specified (fix it) |
Categories | (categorize this paper) |
ISBN(s) | |
DOI | 10.3166/jancl.17.521-543 |
Options |
![]() ![]() ![]() ![]() |
Download options
References found in this work BETA
Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
View all 24 references / Add more references
Citations of this work BETA
No citations found.
Similar books and articles
A Proof–Theoretic Study of the Correspondence of Hybrid Logic and Classical Logic.H. Kushida & M. Okada - 2006 - Journal of Logic, Language and Information 16 (1):35-61.
A Hilbert-Style Axiomatisation for Equational Hybrid Logic.Luís S. Barbosa, Manuel A. Martins & Marta Carreteiro - 2014 - Journal of Logic, Language and Information 23 (1):31-52.
Hybrid Logics with Infinitary Proof Systems.Rineke Verbrugge, Gerard Renardel de Lavalette & Barteld Kooi - unknown
Torben Braüner, Hybrid Logic and its Proof-Theory, Applied Logic Series Volume 37, Springer, 2011, Pp. XIII+231. ISBN: 978-94-007-0001-7 (Hardcover) EURO 99,95, ISBN: 978-94-007-0002-4 (eBook) EURO 99,99. [REVIEW]Melvin Fitting - 2012 - Studia Logica 100 (5):1051-1053.
Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
Pure Extensions, Proof Rules, and Hybrid Axiomatics.Patrick Blackburn & Balder Ten Cate - 2006 - Studia Logica 84 (2):277-322.
Modal Logic, Truth, and the Master Modality.Torben Braüner - 2002 - Journal of Philosophical Logic 31 (4):359-386.
Hybrid Identities and Hybrid Equational Logic.Klaus Denecke - 1995 - Mathematical Logic Quarterly 41 (2):190-196.
Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic.Torben Braüner - 2006 - Journal of Logic, Language and Information 15 (3):179-194.
Proof Theory: A Selection of Papers From the Leeds Proof Theory Programme, 1990.Peter Aczel, Harold Simmons & S. S. Wainer (eds.) - 1992 - Cambridge University Press.
Jean van Heijenoort’s Contributions to Proof Theory and Its History.Irving H. Anellis - 2012 - Logica Universalis 6 (3-4):411-458.
Analytics
Added to PP index
2013-12-30
Total views
16 ( #617,569 of 2,410,082 )
Recent downloads (6 months)
1 ( #541,624 of 2,410,082 )
2013-12-30
Total views
16 ( #617,569 of 2,410,082 )
Recent downloads (6 months)
1 ( #541,624 of 2,410,082 )
How can I increase my downloads?
Downloads