Go to page
 

Bibliographic Metadata

Title
Logic of approximate entailment in quasimetric and in metric spaces
AuthorVetterlein, Thomas
Published in
Soft Computing, 2017, Vol. 21, Issue 17, page 4953-4961
PublishedSpringer, 2017
LanguageEnglish
Document typeJournal Article
Keywords (EN)Representation Theorem / Core Result / Boolean Formula / Approximate Reasoning / Classical Propositional Logic
Project-/ReportnumberI 1923-N25
ISSN1433-7479
URNurn:nbn:at:at-ubl:3-1443 Persistent Identifier (URN)
DOI10.1007/s00500-016-2215-x 
Restriction-Information
 The work is publicly available
Files
Logic of approximate entailment in quasimetric and in metric spaces [0.45 mb]
Links
Reference
Classification
Abstract (English)

It is known that a quasimetric space can be represented by means of a metric space; the points of the former space become closed subsets of the latter one, and the role of the quasimetric is assumed by the Hausdorff quasidistance. In this paper, we show that, in a slightly more special context, a sharpened version of this representation theorem holds. Namely, we assume a quasimetric to fulfil separability in the original sense due to Wilson. Then any quasimetric space can be represented by means of a metric space such that distinct points are assigned disjoint closed subsets.

This result is tailored to the solution of an open problem from the area of approximate reasoning. Following the lines of E. Ruspinis work, the Logic of Approximate Entailment (LAE

) is based on a graded version of the classical entailment relation. We present a proof calculus for LAE and show its completeness with regard to finite theories.

Stats
The PDF-Document has been downloaded 2 times.
License
CC-BY-License (4.0)Creative Commons Attribution 4.0 International License