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International Conference on Logic Programming and Nonmonotonic Reasoning

LPNMR 2017: Logic Programming and Nonmonotonic Reasoning pp 85–100Cite as

A Monotonic View on Reflexive Autoepistemic Reasoning

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10377))

Abstract

This paper introduces a novel monotonic modal logic, able to characterise reflexive autoepistemic reasoning of the nonmonotonic variant of modal logic \(\mathbf {SW5}\): we add a second new modal operator into the original language of \(\mathbf {SW5}\), and show that the resulting formalism called is strong enough to capture the minimal model notion underlying some major forms of nonmonotonic logic among which are autoepistemic logic, default logic, and nonmonotonic logic programming. The paper ends with a discussion of a general strategy, naturally embedding several nonmonotonic logics of similar kinds.

E.I. Su—A similar work was given for nonmonotonic \(\mathbf {KD45}\) in an unpublished paper by Luis Fariñas del Cerro, Andreas Herzig, and Levan Uridia, so special thanks go to them for motivation and some discussions. I am also grateful to the anonymous reviewers for their useful comments. This paper has been supported by the research unit “Centro de Matemática, Aplicações Fundamentais e Investigação Operacional (CMAF-CIO)” at the University of Lisbon, Portugal.

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Notes

  1. 1.

    A cluster is simply an \(\mathbf {S5}\) model in which the accessibility relation is an equivalence relation.

  2. 2.

    Unless specified otherwise, any definition of this paper is given w.r.t. the relation \(\mathcal {T}\).

  3. 3.

    \(\varDelta _{{W' }}\) is the diagonal of \(W' \times W' \), i.e.,  \(\varDelta _{{W' }} = {\{ (a,a) \ :\ a \in W' \}}\).

  4. 4.

    Note that there is no \(\mathbf {F} \)-frame being mapped to (i) a \(\mathbf {K}\)-frame containing more than one cluster structure in it, and (ii) a \(\mathbf {K}\)-frame composed of only a single cluster structure in which \( \mathcal {S}\ne \emptyset \).

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Authors and Affiliations

  1. CMAF-CIO, University of Lisbon, 1749-016, Lisbon, Portugal

    Ezgi Iraz Su

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  1. Ezgi Iraz Su
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Correspondence to Ezgi Iraz Su .

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Editors and Affiliations

  1. Drexel University, Philadelphia, Pennsylvania, USA

    Marcello Balduccini

  2. Aalto University, Espoo, Finland

    Tomi Janhunen

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Su, E.I. (2017). A Monotonic View on Reflexive Autoepistemic Reasoning. In: Balduccini, M., Janhunen, T. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2017. Lecture Notes in Computer Science(), vol 10377. Springer, Cham. https://doi.org/10.1007/978-3-319-61660-5_10

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  • DOI: https://doi.org/10.1007/978-3-319-61660-5_10

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  • Online ISBN: 978-3-319-61660-5

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