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Reasoner = Logical Calculus + Rule Engine

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Abstract

We propose using rule languages to encode complex reasoning algorithms in a declarative way. This approach—which follows the classical slogan “Algorithm = Logic + Control”—promises to turn high-level specifications of logical calculi as systems of inference rules into declarative rule-based models that can be executed on state-of-the-art rule engines. Simple rule languages suffice for simple logics, and we review our results on using Datalog rules to reason in the description logic \(\mathcal {EL}\). For more expressive logics, a suitably expressive yet implementable rule language often seems to be missing. To fill this gap, we consider an extension of Datalog with sets, Datalog(S), that can be executed by modern existential-rule reasoners, and we use it to present a rule-based reasoning calculus for the expressive description logic \(\mathcal {ALC}\).

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Notes

  1. For example, the SAT solver of Howe and King uses the operational block directive of SICStus Prolog to implement “watched literals” [20]; this is an example of traditional (albeit elegant) computer programming where controlling execution details is an important part of the implementation.

  2. A fixed Datalog rule set can be evaluated in P w.r.t. the number of facts, but there are polynomial-time algorithms that cannot be captured by Datalog [1].

  3. https://www.cs.ox.ac.uk/isg/ontologies/

  4. https://github.com/knowsys/rulewerk, formerly VLog4j

  5. A subtle but important difference is that their Datalog\(^{\textsc {S}}\) is based on a sort signature that defines which sets may be considered. Data complexity thus becomes P-complete [30, Thm 2], while it is ExpTime-complete for our Datalog(S).

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Acknowledgements

This work is partly supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) in projects number 389792660 (TRR 248, Center for Perspicuous Systems) and KR 4381/1-1 (Emmy Noether grant DIAMOND), and by the Bundesministerium für Bildung und Forschung (BMBF, Federal Ministry of Education and Research) in the Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI).

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  1. TU Dresden, Dresden, Germany

    David Carral, Irina Dragoste & Markus Krötzsch

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  1. David Carral
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Correspondence to Markus Krötzsch.

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Carral, D., Dragoste, I. & Krötzsch, M. Reasoner = Logical Calculus + Rule Engine. Künstl Intell 34, 453–463 (2020). https://doi.org/10.1007/s13218-020-00667-6

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