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“Sing and Dance!”

Input/Output Logics without Weakening

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Deontic Logic and Normative Systems (DEON 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8554))

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Abstract

Makinson and van der Torre [13] introduce a number of input/output (I/O) logics to reason about conditional norms. The key idea is to make obligations relative to a given set of conditional norms. The meaning of the normative concepts is, then, given in terms of a set of procedures yielding outputs for inputs. Using the same methodology, Stolpe[19,20] has developed some more I/O logics to include systems without the rule of weakening of the output (or principle of inheritance). We extend Stolpe’s account in two directions. First, we show how to make it support reasoning by cases−a common form of reasoning. Second, we show how to inject a new (as we call it, “aggregative”) form of cumulative transitivity, which we think is more suitable for normative reasoning. The main outcomes of the paper are soundness and completeness theorems for the proposed systems with respect to their intended semantics.

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Author information

Authors and Affiliations

  1. University of Luxembourg, Luxembourg

    Xavier Parent & Leendert van der Torre

Authors
  1. Xavier Parent
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  2. Leendert van der Torre
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Editor information

Editors and Affiliations

  1. Department of Philosophy, Northwestern University, Campus Drive, 1880, 60208, Evanston, IL, USA

    Fabrizio Cariani

  2. Department of Computer Science, University of Liverpool, Ashton Building, Ashton Street, L69 3BX, Liverpool, UK

    Davide Grossi

  3. Centre for Logic and Philosophy of Science, Universiteit Gent, Blandijnberg 2, 9000, Gent, Belgium

    Joke Meheus

  4. University of Luxembourg,  6, rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Luxembourg

    Xavier Parent

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© 2014 Springer International Publishing Switzerland

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Parent, X., van der Torre, L. (2014). “Sing and Dance!”. In: Cariani, F., Grossi, D., Meheus, J., Parent, X. (eds) Deontic Logic and Normative Systems. DEON 2014. Lecture Notes in Computer Science(), vol 8554. Springer, Cham. https://doi.org/10.1007/978-3-319-08615-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-08615-6_12

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08614-9

  • Online ISBN: 978-3-319-08615-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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