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Cumulativity Tailored for Nonmonotonic Reasoning

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 9060)

Abstract

In nonmonotonic reasoning, conclusions can be retracted when new pieces of information are incorporated into premises. This contrasts with classical reasoning which is monotonic, i.e., new premises can only increase the set of conclusions that can be drawn. Slightly weaker properties, such as cumulativity and rationality, seem reasonable counterparts of such a monotonicity property for nonmonotonic reasoning but intriguingly it turned out that some major nonmonotonic logics failed to be cumulative. These observations led to the study of variants in hope of restoring cumulativity but not losing other essential properties. In this paper, we take a fresh view on cumulativity by starting from a notion of rule entailment in the context of answer set programs. It turns out that cumulativity can be revived if the expressive precision of rules subject to answer set semantics is fully exploited when new premises are being incorporated. Even stronger properties can be established and we illustrate how the approach can be generalized for major nonmonotonic logics.

Keywords

  • Logic Program
  • Stable Model
  • Integrity Constraint
  • Choice Rule
  • Default Theory

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The support from the Finnish Centre of Excellence in Computational Inference Research (COIN) funded by the Academy of Finland (under grant #251170) is gratefully acknowledged.

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Janhunen, T., Niemelä, I. (2015). Cumulativity Tailored for Nonmonotonic Reasoning. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds) Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation. Lecture Notes in Computer Science(), vol 9060. Springer, Cham. https://doi.org/10.1007/978-3-319-14726-0_7

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  • DOI: https://doi.org/10.1007/978-3-319-14726-0_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14725-3

  • Online ISBN: 978-3-319-14726-0

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