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.
The operator “=” can be represented by “\(\le \)” and “\(\ge \)”.
- 2.
We use different fonts for function and predicate symbols, such as “\(h\)” and “\(\mathsf {bonus}\)” in this example, for clarity.
- 3.
- 4.
More compact encoding can be obtained using choice rules, but for our purposes the current one is sufficient.
- 5.
Disequalities and implications can be represented using the operators “\(\le \)” and “\(\ge \)” [17].
- 6.
A prototype implementation of the mingo \(^r\)Â system and benchmarks can be found under http://research.ics.aalto.fi/software/asp/mingoR.
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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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