Logics of metric spaces

  • Authors:

  • Oliver Kutz;Frank Wolter;Holger Sturm;Nobu-Yuki Suzuki;Michael Zakharyaschev

  • Affiliations:

  • University of Liverpool, Liverpool, U.K.;University of Liverpool, Liverpool, U.K.;Universität Konstanz, Konstanz, Germany;Shizuoka University, Ohya, Shizuoka, Japan;King's College London, Strand, London, U.K.

  • Venue:
  • ACM Transactions on Computational Logic (TOCL)
  • Year:
  • 2003

Quantified Score

Hi-index 0.00

Visualization

Abstract

We investigate the expressive power and computational properties of two different types of languages intended for speaking about distances. First, we consider a first-order language FM the two-variable fragment of which turns out to be undecidable in the class of distance spaces validating the triangular inequality as well as in the class of all metric spaces. Yet, this two-variable fragment is decidable in various weaker classes of distance spaces. Second, we introduce a variable-free modal language MS that, when interpreted in metric spaces, has the same expressive power as the two-variable fragment of FM. We determine natural and expressive fragments of MS which are decidable in various classes of distance spaces validating the triangular inequality, in particular, the class of all metric spaces.