SCIENCE CHINA Information Sciences, Volume 63 , Issue 7 : 172001(2020) https://doi.org/10.1007/s11432-020-2917-1

Unifying logic rules and machine learning for entity enhancing

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  • ReceivedApr 1, 2020
  • AcceptedApr 16, 2020
  • PublishedJun 8, 2020


This paper proposes a notion of entity enhancing, which unifies entity resolution and conflict resolution, to identify tuples that refer to the same real-world entity and at the same time, correct semantic inconsistencies. We propose to unify rule-based and machine learning (ML) methods for entity enhancing, by embedding ML classifiers as predicates in logic rules. We model entity enhancing by extending the chase. We show that the chase warrants correctness justification and the Church-Rosser property. Moreover, we settle fundamental problems associated with entity enhancing, including the enhancing, consistency, satisfiability, and implication problems, ranging from mathsf NPxspace-complete and mathsf coNPxspace-complete to $\Pi_2^p$-complete. Taken together, these provide a new theoretical framework for unifying entity resolution and conflict resolution.


This work was supported in part by Shenzhen Institute of Computing Sciences, Beijing Advanced Innovation Center for Big Data and Brain Computing (Beihang University), Royal Society Wolfson Research Merit Award (Grant No. WRM/R1/180014), European Research Council (Grant No. 652976), Engineering and Physical Sciences Research Council (Grant No. EP/M025268/1).


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  • Table 1  

    Table 1Relation $D_1$ of schema mathsf productxspace

    mathsf tidxspace ${~{\mathsf{~id}}}\xspace$ ${~{\mathsf{~seller}}}\xspace^*$ ${~{\mathsf{~description}}}\xspace^*$ mathsf weightxspace ${~{\mathsf{~type}}}\xspace^*$ mathsf pricexspace ${~{\mathsf{~online\_year}}}\xspace^*$
    $t_1$ $p_1$ $s_1$ MacBook Air $13''$, mid 2019, 1.6 GH Intel i5, 128 GB SSD 1.3 kg computer 8.3K $2019$
    $t_2$ $p_2$ $s_1$ MacBook MVFK2CH/A, 128 GB $1.3~\text{kg}^*$ computer $8.3\text{K}^*$ $2019$
    $t_3$ $p_3$ $s_2$ MacbookAir8,1, i5, 8 GB SDRAM, 128 GB SSD 9.5 kg computer 7.3K $2018$
    $t_4$ $p_4$ $s_1$ MacBook MREE2CH/A, Intel i5, 8 GB LPDDR3, 128 GB $1.3~~\text{kg}^*$ computer 9.6K $2018$
    $t_5$ $p_5$ $s_2$ iMac MRQY2CH/A $27''$, 1 TB 9.5 kg computer 12.9K $2019$
  • Table 2  

    Table 2Relation $D_2$ of schema mathsf shopxspace

    mathsf tidxspace ${~{\mathsf{~id}}}\xspace$ mathsf namexspace ${~{\mathsf{~date\_created}}}\xspace^*$ ${~{\mathsf{~on\_sale\_product}}}\xspace^*$
    $t_6$ $s_1$ Apple official $2015/1/1$ $p_1$
    $t_7$ $s_2$ Apple $2015/1/1$ $p_2$
  • Table 3  

    Table 3Relation $D_3$ of schema mathsf deliveryxspace

    mathsf tidxspace ${~{\mathsf{~id}}}\xspace$ ${~{\mathsf{~item}}}\xspace^*$ ${~{\mathsf{~quantity}}}\xspace^*$ ${~{\mathsf{~city}}}\xspace^*$ mathsf feexspace
    $t_8$ $d_1$ $p_3$5K Beijing $1\text{K}^*$
    $t_9$ $d_2$ $p_5$5K Beijing 3K
  • Table 4  

    Table 4Complexity for entity enhancing and reasoning about mathsf REEsxspace

    Entity enhancing Consistency Satisfiability Implication
    mathsf NPxspace-complete (Theorem 4.2) mathsf coNPxspace-complete (Theorem 4.3) mathsf NPxspace-complete (Theorem 4.5)$\Pi_2^p$-complete (Theorem 4.8)

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