Hybrid logics: Characterization, interpolation and complexity

Journal of Symbolic Logic 66 (3):977-1010 (2001)
Abstract
Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called $\mathscr{H}(\downarrow, @)$ . We show in detail that $\mathscr{H}(\downarrow, @)$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of Ehrenfeucht-Fraisse game, and an enriched notion of bisimulation) and a syntactic characterization (in terms of bounded formulas). The key result to emerge is that $\mathscr{H}(\downarrow, @)$ corresponds to the fragment of first-order logic which is invariant for generated submodels. We then show that $\mathscr{H}(\downarrow, @)$ enjoys (strong) interpolation, provide counterexamples for its finite variable fragments, and show that weak interpolation holds for the sublanguage H(@). Finally, we provide complexity results for H(@) and other fragments and variants, and sharpen known undecidability results for $\mathscr{H}(\downarrow, @)$
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2695090
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 27,636
Through your library
References found in this work BETA
Modal Logic with Names.George Gargov & Valentin Goranko - 1993 - Journal of Philosophical Logic 22 (6):607 - 636.
Hybrid Languages.Patrick Blackburn & Jerry Seligman - 1995 - Journal of Logic, Language and Information 4 (3):251-272.
Hybrid Languages and Temporal Logic.P. Blackburn & M. Tzakova - 1999 - Logic Journal of the IGPL 7 (1):27-54.
Hybrid Completeness.P. Blackburn & M. Tzakova - 1998 - Logic Journal of the IGPL 6 (4):625-650.

View all 6 references / Add more references

Citations of this work BETA
Arthur Prior and Hybrid Logic.Patrick Blackburn - 2006 - Synthese 150 (3):329-372.
Expressive Power of “Now” and “Then” Operators.Igor Yanovich - 2015 - Journal of Logic, Language and Information 24 (1):65-93.

View all 23 citations / Add more citations

Similar books and articles
Hybrid Languages.Patrick Blackburn & Jerry Seligman - 1995 - Journal of Logic, Language and Information 4 (3):251-272.
On Weak and Strong Interpolation in Algebraic Logics.Gábor Sági & Saharon Shelah - 2006 - Journal of Symbolic Logic 71 (1):104 - 118.
The Complexity of Hybrid Logics Over Equivalence Relations.Martin Mundhenk & Thomas Schneider - 2009 - Journal of Logic, Language and Information 18 (4):493-514.
Constructive Interpolation in Hybrid Logic.Patrick Blackburn & Maarten Marx - 2003 - Journal of Symbolic Logic 68 (2):463-480.
Remarks on Gregory's “Actually” Operator.Patrick Blackburn & Maarten Marx - 2002 - Journal of Philosophical Logic 31 (3):281-288.

Monthly downloads

Added to index

2009-01-28

Total downloads

35 ( #146,879 of 2,169,100 )

Recent downloads (6 months)

2 ( #186,455 of 2,169,100 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums