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
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 56,949
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38.
Tonk, Plonk and Plink.Nuel Belnap - 1962 - Analysis 22 (6):130-134.
Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
Labelled Deductive Systems.Dov M. Gabbay - 1996 - Oxford University Press.

View all 24 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

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.
Modal Hybrid Logic.Andrzej Indrzejczak - 2007 - Logic and Logical Philosophy 16 (2-3):147-257.
Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
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.

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 )

How can I increase my downloads?

Downloads

My notes