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International Conference on Applications of Declarative Programming and Knowledge Management

Workshop on Logic Programming

International Workshop on Functional and Constraint Logic Programming

INAP 2013, WLP 2013, WFLP 2013: Declarative Programming and Knowledge Management pp 118–135Cite as

Introducing Real Variables and Integer Objective Functions to Answer Set Programming

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8439))

Abstract

Answer set programming languages have been extended to support linear constraints and objective functions. However, the variables allowed in the constraints and functions are restricted to integer and Boolean domains, respectively. In this paper, we generalize the domain of linear constraints to real numbers and that of objective functions to integers. Since these extensions are based on a translation from logic programs to mixed integer programs, we compare the translation-based answer set programming approach with the native mixed integer programming approach using a number of benchmark problems.

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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Notes

  1. 1.

    The operator “=” can be represented by “\(\le \)” and “\(\ge \)”.

  2. 2.

    We use different fonts for function and predicate symbols, such as “\(h\)” and “\(\mathsf {bonus}\)” in this example, for clarity.

  3. 3.

    Linear and logarithmic encodings can be achieved using cardinality constraints [6, 18] and bit vectors [15], respectively. But both are more complex than the given ASP(LC) encoding.

  4. 4.

    More compact encoding can be obtained using choice rules, but for our purposes the current one is sufficient.

  5. 5.

    Disequalities and implications can be represented using the operators “\(\le \)” and “\(\ge \)” [17].

  6. 6.

    A prototype implementation of the mingo \(^r\) system and benchmarks can be found under http://research.ics.aalto.fi/software/asp/mingoR.

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Author information

Authors and Affiliations

  1. Helsinki Institute for Information Technology HIIT, Department of Information and Computer Science, Aalto University, FI-00076, Aalto, Finland

    Guohua Liu, Tomi Janhunen & Ilkka Niemelä

Authors
  1. Guohua Liu
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  2. Tomi Janhunen
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  3. Ilkka Niemelä
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Corresponding author

Correspondence to Tomi Janhunen .

Editor information

Editors and Affiliations

  1. Universität Kiel, Kiel, Germany

    Michael Hanus

  2. CRACS & INESC-Porto LA, University of Porto, Porto, Portugal

    Ricardo Rocha

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Liu, G., Janhunen, T., Niemelä, I. (2014). Introducing Real Variables and Integer Objective Functions to Answer Set Programming. In: Hanus, M., Rocha, R. (eds) Declarative Programming and Knowledge Management. INAP WLP WFLP 2013 2013 2013. Lecture Notes in Computer Science(), vol 8439. Springer, Cham. https://doi.org/10.1007/978-3-319-08909-6_8

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  • DOI: https://doi.org/10.1007/978-3-319-08909-6_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08908-9

  • Online ISBN: 978-3-319-08909-6

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