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International Conference on Logic Programming and Nonmonotonic Reasoning

LPNMR 2017: Logic Programming and Nonmonotonic Reasoning pp 205–211Cite as

Answer Set Programming with Graded Modality

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

Abstract

Answer set programming with graded modality (ASP\(^{\text {GM}}\)) introduced in [6] provides an intuitive way for expressing modal concepts “at least as many as......” as well as “at most as many as......”, and defaults. This paper studies the semantics of ASP\(^{\text {GM}}\) and investigates its connection to the most recent language of epistemic specification (ASP\(^{\text {KM}}\)) proposed in [3] and the answer set programming with epistemic negation (ASP\(^{\text {NOT}}\)) presented in [5]. Particularly, we define a new approach to evaluating graded modalities in ASP\(^{\text {GM}}\) such that ASP\(^{\text {GM}}\) is compatible with ASP\(^{\text {KM}}\) as well as ASP\(^{\text {NOT}}\) at the semantic level.

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Notes

  1. 1.

    Here, we view not not l as a representation of \(not~l^\prime \) where we have \(l^\prime \leftarrow not~l\) and \(l^\prime \) is a fresh literal. It is worthwhile to note that CLINGO [8] is able to deal with not not.

References

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  2. Gelfond, M.: Logic programming and reasoning with incomplete information. Ann. Math. Artif. Intell. 12(1–2), 89–116 (1994)

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  3. Kahl, P.T.: Refining the semantics for epistemic logic programs, Ph.D. thesis, Texas Tech University, USA (2014)

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  4. Farias del Cerro, L., Herzig, A., Su, E.I.: Epistemic equilibrium logic. In: IJCAI-2015, pp. 2964–2970 (2015)

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  5. Shen, Y.D., Eiter, T.: Evaluating epistemic negation in answer set programming. Artif. Intell. 237, 115–135 (2016)

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  6. Zhang, Z., Zhang, S.: Logic programming with graded modality. In: Calimeri, F., Ianni, G., Truszczynski, M. (eds.) LPNMR 2015. LNCS (LNAI), vol. 9345, pp. 517–530. Springer, Cham (2015). doi:10.1007/978-3-319-23264-5_43

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  7. Gelfond, M.: New semantics for epistemic specifications. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS (LNAI), vol. 6645, pp. 260–265. Springer, Heidelberg (2011). doi:10.1007/978-3-642-20895-9_29

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  8. http://sourceforge.net/projects/potassco/files/guide/2.0/guide-2.0.pdf

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Acknowledgments

This work was supported by the National High Technology Research and Development Program of China (Grant No. 2015AA015406), and the National Science Foundation of China (Grant No. 60803061).

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Authors and Affiliations

  1. School of Computer Science and Engineering, Southeast University, Nanjing, China

    Zhizheng Zhang

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  1. Zhizheng Zhang
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Correspondence to Zhizheng Zhang .

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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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Zhang, Z. (2017). Answer Set Programming with Graded Modality. 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_18

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  • DOI: https://doi.org/10.1007/978-3-319-61660-5_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61659-9

  • Online ISBN: 978-3-319-61660-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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