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Qualitative and Semi-Quantitative Inductive Reasoning with Conditionals

Technical Project Report

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Abstract

Conditionals like “birds fly—if bird then fly” are crucial for commonsense reasoning. In this technical project report we show that conditional logics provide a powerful formal framework that helps understanding if-then sentences in a way that is much closer to human reasoning than classical logic and allows for high-quality reasoning methods. We describe methods that inductively generate models from conditional knowledge bases. For this, we use both qualitative (like preferential models) and semi-quantitative (like Spohn’s ranking functions) semantics. We show similarities and differences between the resulting inference relations with respect to formal properties. We further report on two graphical methods on top of the ranking approaches which allow to decompose the models into smaller, more feasible components and allow for local inferences.

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Notes

  1. i.e., we use numbers in a qualitative way.

  2. http://airconditionals.cs.tu-dortmund.de.

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Authors and Affiliations

  1. Technische Universität Dortmund, Lehrstuhl Informatik 1, Dortmund, Germany

    Christian Eichhorn & Gabriele Kern-Isberner

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  1. Christian Eichhorn
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  2. Gabriele Kern-Isberner
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Correspondence to Christian Eichhorn.

Additional information

We thank the anonymous referees for their valuable hints that helped us improving the paper. This work was supported by grant KI\(\;1413/5-1\) to Gabriele Kern-Isberner from the Deutsche Forschungsgemeinschaft (DFG) as part of the priority program “New Frameworks of Rationality” (SPP 1516). Christian Eichhorn is supported by this Grant.

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Eichhorn, C., Kern-Isberner, G. Qualitative and Semi-Quantitative Inductive Reasoning with Conditionals. Künstl Intell 29, 279–289 (2015). https://doi.org/10.1007/s13218-015-0376-x

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