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An Introduction to Answer Set Programming and Some of Its Extensions

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Reasoning Web. Declarative Artificial Intelligence (Reasoning Web 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12258))

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Abstract

Answer Set Programming (ASP) is a rule-based language rooted in traditional Logic Programming, Databases, Knowledge Representation, and Nonmonotonic Reasoning. It offers a flexible language for declarative problem solving, with support of efficient general-purpose solvers and reasoners. The larger part of this article provides an introduction to ASP, with a historical perspective, a definition of the core language, a guideline to knowledge representation, and an overview of existing ASP solvers. One part focuses on one commonly used feature: aggregates and generalized atoms. The inclusion of aggregates in ASP (and Logic Programming at large) has long been motivated, however there are some issues with semantics to be addressed, in particular when aggregates occur in recursive definitions. Very similar considerations are needed when coupling ASP with other formalisms, which we collectively refer to as “generalized atoms”. An overview of these semantic challenges and proposals for addressing them is provided, along with an overview of complexity results and system support.

Parts of this work are based on [70].

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Notes

  1. 1.

    https://www.mat.unical.it/aspcomp2011/files/Corelang2004.pdf.

  2. 2.

    In positive programs negation as failure (\(\mathrm {not} \)) does not occur, while strong negation (\(\lnot \)) may be present.

  3. 3.

    Actually, since the language does not contain function symbols and since rules are required to be safe, this extra constant is not needed. However, we have kept the classic definition in order to avoid confusion.

  4. 4.

    A substitution here is a set of instructions for replacing variables by terms (here constants). An application of these replacements is denoted by postfixing the substitution to the structure, in which the replacements should be applied.

  5. 5.

    In the example, we adopted the syntax of the DLV system, the same aggregate functions can be specified also by exploiting other ASP dialects.

  6. 6.

    Some ASP variants use choice rules as guessing part (see   [133, 154, 159]), Moreover, in some cases, it is possible to emulate disjunction by unstratified normal rules by “shifting” the disjunction to the body [21, 61, 116], but this is not possible in general.

  7. 7.

    The input is usually read from text files, but some systems also interface to relational databases for retrieving facts stored in relational tables.

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Acknowledgements

The author thanks all his co-authors over the years, for the discussions and the work that laid the foundation to this overview; in particular Nicola Leone and Francesco Ricca, with whom I co-authored a description, on which the present work has been partially based. The author would also like to thank the ASP community at large, it is great to be part of such a stimulating and critical, yet amiable crowd.

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    Wolfgang Faber

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    Marco Manna

  2. School of Informatics, University of Edinburgh, Edinburgh, UK

    Andreas Pieris

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Faber, W. (2020). An Introduction to Answer Set Programming and Some of Its Extensions. In: Manna, M., Pieris, A. (eds) Reasoning Web. Declarative Artificial Intelligence. Reasoning Web 2020. Lecture Notes in Computer Science(), vol 12258. Springer, Cham. https://doi.org/10.1007/978-3-030-60067-9_6

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