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Unified Decomposition-Aggregation (UDA) Rules: Dynamic, Schematic, Novel Axioms

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Book cover Intelligent Computer Mathematics (CICM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13467))

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Abstract

We introduce Unified Decomposition-Aggregation (UDA) Rules. They are a family of axiom schemata that are instantiated at run-time to add new axioms to a logical theory. These new axioms are implications, whose preconditions will be constructed from an analysis of the goal to be proved and the theory in which it is to be proved. We illustrate their application to query answering using the FRANK system.

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Notes

  1. 1.

    Previously called decomposition rules.

  2. 2.

    See https://en.wikipedia.org/wiki/Association_list (last accessed: 02-02-2022). Alists are not lists but sets, but the ‘alist’ terminology has, unfortunately, become standard.

  3. 3.

    https://en.wikipedia.org/wiki/Epsilon_calculus accessed on 02.02.2022.

  4. 4.

    Although not for any of the examples in this paper.

  5. 5.

    Or similar, depending on the statistical methods used.

  6. 6.

    Note that the temporal rule can also use non-statistical aggregation functions, e.g., temp(max) could be used to find the maximum value of a property among a set of times.

  7. 7.

    https://en.wikipedia.org/wiki/68-95-99.7_rule accessed on 12.5.22.

  8. 8.

    We are grateful to an anonymous reviewer for pointing out this analogy and suggesting that we discuss it here.

References

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Acknowledgements

Thanks to Nicholas Ferguson, Thomas Fletcher, Xue Li, Ruqui Zhu and five anonymous reviewers for feedback on an earlier draft. This research has been supported by Huawei grants CIENG4721/LSC and HO2017050001B8s. For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission.

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Authors and Affiliations

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

    Alan Bundy & Kwabena Nuamah

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  1. Alan Bundy
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  2. Kwabena Nuamah
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Correspondence to Alan Bundy .

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Editors and Affiliations

  1. Imperial College London, London, UK

    Kevin Buzzard

  2. Johannes Kepler University Linz, Linz, Austria

    Temur Kutsia

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Bundy, A., Nuamah, K. (2022). Unified Decomposition-Aggregation (UDA) Rules: Dynamic, Schematic, Novel Axioms. In: Buzzard, K., Kutsia, T. (eds) Intelligent Computer Mathematics. CICM 2022. Lecture Notes in Computer Science(), vol 13467. Springer, Cham. https://doi.org/10.1007/978-3-031-16681-5_15

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  • DOI: https://doi.org/10.1007/978-3-031-16681-5_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-16680-8

  • Online ISBN: 978-3-031-16681-5

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