Journal of Symbolic Logic

Notions of Locality and Their Logical Characterizations Over Finite Models

Lauri Hella, Leonid Libkin, and Juha Nurmonen

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.

Abstract

Many known tools for proving expressibility bounds for first-order logic are based on one of several locality properties. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hanf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of the easiest tools for proving expressibility bounds. These results apply beyond the first-order case. We use them to derive expressibility bounds for first-order logic with unary quantifiers and counting. We also characterize the notions of locality on structures of small degree.

Article information

Source
J. Symbolic Logic, Volume 64, Issue 4 (1999), 1751-1773.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745951

Mathematical Reviews number (MathSciNet)
MR1780083

Zentralblatt MATH identifier
0946.03012

JSTOR
links.jstor.org

Citation

Hella, Lauri; Libkin, Leonid; Nurmonen, Juha. Notions of Locality and Their Logical Characterizations Over Finite Models. J. Symbolic Logic 64 (1999), no. 4, 1751--1773. https://projecteuclid.org/euclid.jsl/1183745951


Export citation