Interpolation and Definability in Guarded Fragments

Studia Logica 70 (3):373-409 (2002)
  Copy   BIBTEX

Abstract

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,271

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

A note on graded modal logic.Maarten de Rijke - 2000 - Studia Logica 64 (2):271-283.
Guarded fragments with constants.Balder ten Cate & Massimo Franceschet - 2005 - Journal of Logic 14 (3):281-288.
Leibniz filters revisited.Ramon Jansana - 2003 - Studia Logica 75 (3):305 - 317.
Guarded fragments with constants.Balder ten Cate & Massimo Franceschet - 2005 - Journal of Logic, Language and Information 14 (3):281-288.
On the restraining power of guards.Erich Grädel - 1999 - Journal of Symbolic Logic 64 (4):1719-1742.

Analytics

Added to PP
2016-02-14

Downloads
21 (#711,668)

6 months
7 (#411,145)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Interpolation for extended modal languages.Balder ten Cate - 2005 - Journal of Symbolic Logic 70 (1):223-234.
Guards, Bounds, and generalized semantics.Johan van Benthem - 2005 - Journal of Logic, Language and Information 14 (3):263-279.
Guarded fragments with constants.Balder ten Cate & Massimo Franceschet - 2005 - Journal of Logic 14 (3):281-288.
The Semijoin Algebra and the Guarded Fragment.Dirk Leinders, Maarten Marx, Jerzy Tyszkiewicz & Jan Bussche - 2005 - Journal of Logic, Language and Information 14 (3):331-343.

View all 7 citations / Add more citations

References found in this work

No references found.

Add more references