KI - Künstliche Intelligenz

, Volume 31, Issue 1, pp 41–52

A Practical Comparison of Qualitative Inferences with Preferred Ranking Models

  • Christoph Beierle
  • Christian Eichhorn
  • Steven Kutsch
Technical Contribution

DOI: 10.1007/s13218-016-0453-9

Cite this article as:
Beierle, C., Eichhorn, C. & Kutsch, S. Künstl Intell (2017) 31: 41. doi:10.1007/s13218-016-0453-9


When reasoning qualitatively from a conditional knowledge base, two established approaches are system Z and p-entailment. The latter infers skeptically over all ranking models of the knowledge base, while system Z uses the unique pareto-minimal ranking model for the inference relations. Between these two extremes of using all or just one ranking model, the approach of c-representations generates a subset of all ranking models with certain constraints. Recent work shows that skeptical inference over all c-representations of a knowledge base includes and extends p-entailment. In this paper, we follow the idea of using preferred models of the knowledge base instead of the set of all models as a base for the inference relation. We employ different minimality constraints for c-representations and demonstrate inference relations from sets of preferred c-representations with respect to these constraints. We present a practical tool for automatic c-inference that is based on a high-level, declarative constraint-logic programming approach. Using our implementation, we illustrate that different minimality constraints lead to inference relations that differ mutually as well as from system Z and p-entailment.


Conditional logic Qualitative conditional Default rule Ranking function C-representation C-inference System Z P-entailment 

Funding information

Funder NameGrant NumberFunding Note
  • Grant KI1413/5-1

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Christoph Beierle
    • 1
  • Christian Eichhorn
    • 2
  • Steven Kutsch
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceFernUniversität in HagenHagenGermany
  2. 2.Department of Computer ScienceTechnische Universität DortmundDortmundGermany

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