PP-1999-07: Areces, Carlos and Blackburn, Patrick and Marx, Maarten (1999) Hybrid Logics. Characterization, Interpolation and Complexity. [Report]
![[thumbnail of Full Text]](https://eprints.illc.uva.nl/style/images/fileicons/text.png) |
Text (Full Text)
PP-1999-07.text.ps.gz Download (178kB) |
|
Text (Abstract)
PP-1999-07.abstract.txt Download (1kB) |
Abstract
Hybrid languages are extended modal languages which can refer to (or even
quantify over) worlds. The use of strong hybrid languages dates back to at
least \cite{prio:past67}, but recent work (for example \cite{blac:hybr98},
\cite{blac:hybr98a}) has focused on a more constrained system called
$\mathcal{H}(\downarrow,@)$. The purpose of the present paper is to show
in detail that $\mathcal{H}(\downarrow,@)$ is a modally natural system.
We begin by studying its expressivity, and provide both model theoretic
characterizations (via a restricted notion of Ehrenfeucht-Fra\"{\i}ss\'e
game, and an enriched notion of bisimulation) and a syntactic characteri-
zation (in terms of bounded formulas). The key result to emerge is that
$\mathcal{H}(\downarrow,@)$ corresponds precisely to the first-order
fragment which is invariant for generated submodels. We further establish
that $\mathcal{H}(\downarrow,@)$ has (strong) interpolation, and provide
failure results in the finite variable fragments. We also show that weak
interpolation holds for the sublanguage $\mathcal{H}(@)$, and provide
complexity results for $\mathcal{H}(@)$ and other fragments and variants
(the full logic being undecidable).
| Item Type: | Report |
|---|---|
| Report Nr: | PP-1999-07 |
| Series Name: | Prepublication (PP) Series |
| Year: | 1999 |
| Date Deposited: | 12 Oct 2016 14:36 |
| Last Modified: | 12 Oct 2016 14:36 |
| URI: | https://eprints.illc.uva.nl/id/eprint/7 |
Actions (login required)
 |
View Item |
