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Decision-Making Support Using Nonmonotonic Probabilistic Reasoning

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Intelligent Decision Technologies 2019

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 142))

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Abstract

The goal of this paper is to introduce a decision-making support by rule-based nonmonotonic reasoning enhanced with probabilities. As a suitable rule-based tool, we analyze answer set programming (Asp) and explore its probabilistic extension that permits the use of probabilistic expressions of two types. The first type represents an externally given prior probability distribution on literals in an answer set program \(\varPi \). The second type represents a posterior distribution conditioned on individual decisions and choices made, together with their consequences represented by answer sets of \(\varPi \). The ability to compare aspects of both the prior and posterior probabilities in the language of the program \(\varPi \) has interesting uses in filtering solutions/decisions one is interested in. A formal characterization of this probabilistic extension to Asp is provided in addition to examples demonstrating its potential use. It is also shown that the proposed techniques do not increase the complexity of standard Asp-based reasoning.

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Notes

  1. 1.

    If \(B=\{\}\) then \(\ell \,|\,B\) is abbreviated to B.

  2. 2.

    Note that default negation is not allowed here, too.

  3. 3.

    Here the component \(\pi '\) of \(\varPi /A\) contains only rules for which Definition 4.4 is applicable.

  4. 4.

    This is, of course, a well-known complexity theoretical technique.

  5. 5.

    Of course, neither Bayesian networks nor Problog are parts of Pasp. They are used here to illustrate possible external sources, representing \(P()\). We only need to query them no matter how they are implemented.

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Acknowledgements

I would like to thank Patrick Doherty for discussions and cooperation related to this paper. My thanks are also due to Barbara Dunin-Kȩplicz for helpful comments and suggestions. This work is supported by the grant 2017/27/B/ST6/02018 of the National Science Centre Poland, the ELLIIT Network Organization for Information and Communication Technology, and the Swedish FSR (SymbiKBot Project).

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Szałas

  2. Department of Computer and Information Science, Linköping University, 581 83, Linköping, Sweden

    Andrzej Szałas

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  1. Andrzej Szałas
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Correspondence to Andrzej Szałas .

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Editors and Affiliations

  1. Department of Information Systems, Gdynia Maritime University, Gdynia, Poland

    Ireneusz Czarnowski

  2. Bournemouth University and KES International, Poole, Dorset, UK

    Robert J. Howlett

  3. University of Canberra, Canberra, ACT, Australia

    Lakhmi C. Jain

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Szałas, A. (2020). Decision-Making Support Using Nonmonotonic Probabilistic Reasoning. In: Czarnowski, I., Howlett, R., Jain, L. (eds) Intelligent Decision Technologies 2019. Smart Innovation, Systems and Technologies, vol 142. Springer, Singapore. https://doi.org/10.1007/978-981-13-8311-3_4

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