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Computing Strong and Weak Permissions in Defeasible Logic

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Abstract

In this paper we propose an extension of Defeasible Logic to represent and compute different concepts of defeasible permission. In particular, we discuss some types of explicit permissive norms that work as exceptions to opposite obligations or encode permissive rights. Moreover, we show how strong permissions can be represented both with, and without introducing a new consequence relation for inferring conclusions from explicit permissive norms. Finally, we illustrate how a preference operator applicable to contrary-to-duty obligations can be combined with a new operator representing ordered sequences of strong permissions. The logical system is studied from a computational standpoint and is shown to have linear computational complexity.

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Notes

  1. As it is well-known, in a non-reflexive modal logic, □a does not imply a, where □ is a modal operator.

  2. The idea of using defeaters to introduce permissions was introduced in [16].

  3. Hence, we speak here of entitlements or rights, as corresponding to options for exercising the same general permissive right to compensation. In this perspective, we can model them as permissions on one party (in this case the copyright owner) generating an obligation on another party (in this case the infringer). This is in line with the classic conception of rights proposed, for instance, in [19], which does not properly view them as powers: a power is typically required there to generate further normative effects (such as duties, juridical relations, etc.). For a more detailed discussion on these issues, see [25].

  4. This in general might be prohibited based on contractual conditions or by other laws.

  5. The strong negation of a formula is closely related to the function that simplifies a formula by moving all negations to an inner most position in the resulting formula, and replaces the positive tags with respective negative tags, and vice versa.

  6. Situations like O∼l ⇒ O ∼l, where the proof conditions will generate a loop without introducing a proof.

  7. Notice that the rules in conditions (2.2) and (2.3.3) are different rules: they form a team that can defeat teams of rules for the opposite.

  8. A defeasible theory is finite when the sets of facts and rules are finite.

  9. Notice that we do not remove any negative modal literal from HB by definition of modal Herbrand Base.

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Acknowledgments

This work is an extended and revised version of the paper presented at Jurix 2011 [10]. We thank the anonymous referees for their valuable comments.

NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy, the Australian Research Council through the ICT Centre of Excellence program and the Queensland Government.

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Authors and Affiliations

  1. NICTA, Queensland Research Laboratory, Brisbane, Australia

    Guido Governatori, Francesco Olivieri & Simone Scannapieco

  2. Department of Computer Science, University of Verona, Verona, Italy

    Francesco Olivieri & Simone Scannapieco

  3. Institute for Integrated and Intelligent Systems, Griffith University, Nathan, Queensland, Australia

    Francesco Olivieri & Simone Scannapieco

  4. CIRSFID, University of Bologna, Bologna, Italy

    Antonino Rotolo

Authors
  1. Guido Governatori
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  2. Francesco Olivieri
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  3. Antonino Rotolo
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  4. Simone Scannapieco
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Correspondence to Guido Governatori.

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Governatori, G., Olivieri, F., Rotolo, A. et al. Computing Strong and Weak Permissions in Defeasible Logic. J Philos Logic 42, 799–829 (2013). https://doi.org/10.1007/s10992-013-9295-1

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