Abstract
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.
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Acknowledgements
We are grateful to all our students who have been involved in the implementation of the software systems described here, in particular to Karl Södler, Martin Austen, and Fadil Kallat. We also thank the anonymous reviewers of this article for their detailed and helpful comments.
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Christian Eichhorn is supported by DFG-Grant KI1413/5-1 of Prof. Dr. Gabriele Kern-Isberner as part of the priority program “New Frameworks of Rationality” (SPP 1516).
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Beierle, C., Eichhorn, C. & Kutsch, S. A Practical Comparison of Qualitative Inferences with Preferred Ranking Models. Künstl Intell 31, 41–52 (2017). https://doi.org/10.1007/s13218-016-0453-9
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DOI: https://doi.org/10.1007/s13218-016-0453-9