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From Input/Output Logics to Conditional Logics via Sequents – with Provers

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12842))

Abstract

We consider cut-free sequent calculi for a number of deontic logics from the family of Input/Output logics. These sequent calculi provide a correspondence to the flat fragment of certain conditional logics. Two of the introduced calculi are non-standard in that they include non-derivability statements, and hence are interesting also from a purely technical perspective. We further modularise the calculi in an extended sequent framework. Proof search in the extended calculi is implemented in Prolog, providing seemingly the first automated reasoning systems for some of the considered logics.

This work has been supported by BRISE-Vienna (UIA04-081), a European Union Urban Innovative Actions project.

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Notes

  1. 1.

    See https://www.swi-prolog.org.

  2. 2.

    See http://subsell.logic.at/bprover/iocondprover/.

  3. 3.

    See https://github.com/blellmann/iocondprover.

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Acknowledgements

This article would not have been possible without the many discussions on the topic with Leon van der Torre. I also thank the reviewers for their thorough reading and comments which helped to improve the article.

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Authors and Affiliations

  1. TU Wien, Vienna, Austria

    Björn Lellmann

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  1. Björn Lellmann
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  1. University of Birmingham, Birmingham, UK

    Anupam Das

  2. University of Genoa, Genoa, Italy

    Sara Negri

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Lellmann, B. (2021). From Input/Output Logics to Conditional Logics via Sequents – with Provers. In: Das, A., Negri, S. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2021. Lecture Notes in Computer Science(), vol 12842. Springer, Cham. https://doi.org/10.1007/978-3-030-86059-2_9

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  • DOI: https://doi.org/10.1007/978-3-030-86059-2_9

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