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A Formal Theory of Justifications

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Logic Programming and Nonmonotonic Reasoning (LPNMR 2015)

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

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Abstract

We develop an abstract theory of justifications suitable for describing the semantics of a range of logics in knowledge representation, computational and mathematical logic. A theory or program in one of these logics induces a semantical structure called a justification frame. Such a justification frame defines a class of justifications each of which embodies a potential reason why its facts are true. By defining various evaluation functions for these justifications, a range of different semantics are obtained. By allowing nesting of justification frames, various language constructs can be integrated in a seamless way. The theory provides elegant and compact formalisations of existing and new semantics in logics of various areas, showing unexpected commonalities and interrelations, and creating opportunities for new expressive knowledge representation formalisms.

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Notes

  1. 1.

    Negation in the head of (extended) answer set programs is different from the negation studied here, and the justification semantics defined below is not directly suitable to compute answer sets of programs with explicit negation. We focus on systems where the rules for facts and their negations are complementary, hence negation is classical. In contrast, rules of ASP for negative literals are independent of those for positive literals.

  2. 2.

    By dropping the constraint that \({\mathcal {F}_o}\) consists of logical facts only, we obtain extensions of all main semantics for a parameterized variant of logic programming.

  3. 3.

    This should not be confused with the nested logic programs of [22], where nesting refers to the expressions inside a logic program rule, and not sets of rules being nested altogether.

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Authors and Affiliations

  1. Department of Computer Science, K.U. Leuven, 3001, Heverlee, Belgium

    Marc Denecker

  2. Computer Science Institute, Leipzig University, Leipzig, Germany

    Gerhard Brewka & Hannes Strass

Authors
  1. Marc Denecker
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  2. Gerhard Brewka
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  3. Hannes Strass
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Correspondence to Marc Denecker .

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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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Denecker, M., Brewka, G., Strass, H. (2015). A Formal Theory of Justifications. 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_22

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  • DOI: https://doi.org/10.1007/978-3-319-23264-5_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23263-8

  • Online ISBN: 978-3-319-23264-5

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