Interpolation and definability in guarded fragments

Studia Logica 70 (3):373 - 409 (2002)
The guarded fragment (GF) was introduced by Andréka, van Benthem and Németi as a fragment of first order logic which combines a great expressive power with nice, modal behavior. It consists of relational first order formulas whose quantifiers are relativized by atoms in a certain way. Slightly generalizing the admissible relativizations yields the packed fragment (PF). In this paper we investigate interpolation and definability in these fragments. We first show that the interpolation property of first order logic fails in restriction to GF and PF. However, each of these fragments turns out to have an alternative interpolation property that closely resembles the interpolation property usually studied in modal logic. These results are strong enough to entail the Beth definability property for GF and PF. Even better, every guarded or packed finite variable fragment has the Beth property. For interpolation, we characterize exactly which finite variable fragments of GF and PF enjoy this property.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
Categories (categorize this paper)
 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
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 24,479
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

No references found.

Add more references

Citations of this work BETA
Johan van Benthem (2005). Guards, Bounds, and Generalized Semantics. Journal of Logic, Language and Information 14 (3):263-279.
Balder ten Cate & Massimo Franceschet (2005). Guarded Fragments with Constants. Journal of Logic, Language and Information 14 (3):281-288.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

15 ( #296,524 of 1,925,795 )

Recent downloads (6 months)

2 ( #308,704 of 1,925,795 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.