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MV-Datalog+-: Effective Rule-based Reasoning with Uncertain Observations

Published online by Cambridge University Press:  26 July 2022

MATTHIAS LANZINGER ,
STEFANO SFERRAZZA Open the ORCID record for STEFANO SFERRAZZA [Opens in a new window]  and
GEORG GOTTLOB
MATTHIAS LANZINGER
Affiliation:
University of Oxford, Oxford OX1 2JD, UK (e-mail: matthias.lanzinger@cs.ox.ac.uk)
STEFANO SFERRAZZA
Affiliation:
University of Oxford, Oxford OX1 2JD, UK, Technische Universität Wien, Vienna, Austria (e-mail: stefano.sferrazza@cs.ox.ac.uk)
GEORG GOTTLOB
Affiliation:
University of Oxford, Oxford OX1 2JD, UK (e-mail: georg.gottlob@cs.ox.ac.uk)
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Abstract

Modern applications combine information from a great variety of sources. Oftentimes, some of these sources, like machine-learning systems, are not strictly binary but associated with some degree of (lack of) confidence in the observation. We propose MV-Datalog and $\mathrm{MV-Datalog}^\pm$ as extensions of Datalog and $\mathrm{Datalog}^\pm$ , respectively, to the fuzzy semantics of infinite-valued Łukasiewicz logic $\mathbf{L}$ as languages for effectively reasoning in scenarios where such uncertain observations occur. We show that the semantics of MV-Datalog exhibits similar model theoretic properties as Datalog. In particular, we show that (fuzzy) entailment can be decided via minimal fuzzy models. We show that when they exist, such minimal fuzzy models are unique and can be characterised in terms of a linear optimisation problem over the output of a fixed-point procedure. On the basis of this characterisation, we propose similar many-valued semantics for rules with existential quantification in the head, extending $\mathrm{Datalog}^\pm$ .

Keywords

Datalogfuzzy logic programminglogic programmingŁukasiewiczlogicuncertainty in AIDatalog±
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 22 , Issue 5: 38th International Conference on Logic Programming Special Issue II , September 2022 , pp. 678 - 692
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

*

Stefano Sferrazza was supported by the Austrian Science Fund (FWF):P30930. Georg Gottlob is a Royal Society Research Professor and acknowledges support by the Royal Society in this role through the “RAISON DATA” project (Reference No. RP\R1\201074). Matthias Lanzinger acknowledges support by the Royal Society “RAISON DATA” project (Reference No. RP\R1\201074).

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