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A New Computational Logic Approach to Reason with Conditionals

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Book cover Logic Programming and Nonmonotonic Reasoning (LPNMR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9345))

Abstract

We present a new approach to evaluate conditionals in human reasoning. This approach is based on the weak completion semantics which has been successfully applied to adequately model various other human reasoning tasks in the past. The main idea is to explicitly consider the case, where the condition of a conditional is unknown with respect to some background knowledge, and to evaluate it with minimal revision followed by abduction. We formally compare our approach to a recent approach by Schulz and demonstrate that our proposal is superior in that it can handle more human reasoning tasks.

The authors are mentioned in alphabetical order.

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Notes

  1. 1.

    This and other definitions are controversially discussed within the fields of philosophy and psychology [14]. Some require, that counterfactuals must be in the subjunctive mood or can only be evaluated in a state that is different wrt the current one [43].

  2. 2.

    We consider weak completion semantics and, hence, a clause of the form \(A \leftarrow \bot \) is turned into \(A \leftrightarrow \bot \) provided that this is the only clause in the definition of A.

  3. 3.

    Note that undefined atoms are not identified with \(\bot \) as in the completion of \(\mathcal{P}\) [5].

  4. 4.

    In this section, the abnormality predicates are not needed. We have kept them to be in line with our general approach to model human reasoning episodes (see e.g. [7]) and to be able to extend the example in the future by, for example, considering the case that the captain is not law-abiding or that a rifle is malfunctioning.

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Acknowledgements

We like to thank Luís Moniz Pereira, Bob Kowalski and Marco Ragni for many discussions and comments on earlier drafts of our work.

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Authors and Affiliations

  1. International Center for Computational Logic, TU Dresden, 01062, Dresden, Germany

    Emmanuelle-Anna Dietz & Steffen Hölldobler

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  1. Emmanuelle-Anna Dietz
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  2. Steffen Hölldobler
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Correspondence to Emmanuelle-Anna Dietz .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Francesco Calimeri

  2. University of Calabria, Rende, Italy

    Giovambattista Ianni

  3. University of Kentucky Dept. Computer Science, Lexington, Kentucky, USA

    Miroslaw Truszczynski

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Dietz, EA., Hölldobler, S. (2015). A New Computational Logic Approach to Reason with Conditionals. In: Calimeri, F., Ianni, G., Truszczynski, M. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2015. Lecture Notes in Computer Science(), vol 9345. Springer, Cham. https://doi.org/10.1007/978-3-319-23264-5_23

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  • DOI: https://doi.org/10.1007/978-3-319-23264-5_23

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