Family Link Detection in Uncertain Settings with MV-Datalog+-

Abstract

We report on a novel work-in-progress system for inferring family links in company ownership graphs. Our system combines fuzzy observations of possible family links from anagraphic data with MV-Datalog± , a new framework for many-valued logical reasoning in Datalog± . With this approach we achieve levels of flexibility and explainability benefits that is dificult to match by current Machine Learning methods. We describe the key challenges, main components of our approach, and experimentally illustrate its efectiveness at this early stage in its development.

1. Introduction

Company ownership graphs play a central role for central banks, financial authorities and national statistical ofices [ 1, 2, 3, 4 ] and represent a valuable tool for solving a wide range of problems in the context of banking supervision, credit-worthiness evaluation, anti-money laundering, insurance fraud detection, economic and statistical research. One particular such ownership graph that we consider in this paper is the Enterprise Knowledge Graph of Italian companies [ 5 ], in which people and companies are the nodes, while the (labelled) edges represent Figure 1: A typical case of hidden close link where cannot the fraction of company shares owned by a person or a act as guarantor for due to the family relationship between company. and

One of the main challenges for detecting regulatory issues in the Enterprise Knowledge Graph is the obfuscation of actual company ownership. Such obfuscation pany and , we can infer that even if and do can be highly problematic. For example, according to not strictly fulfil the definition of close link, we should European Central Bank regulations, company is not prevent both companies from being the guarantor of the eligible as a guarantor for if it is too “close” to it in other. However, company ownership graphs often are determs of ownership [ 6 ]. It is therefore important to iden- rived from data where family relationships are not explictify potential close links in company ownership graphs itly available and must be reconstructed through other to efectively detect problematic constructs. One particu- methods. The lack of public data makes the task of finding larly common type of potential close link is through fam- family links highly challenging since civil registers can ily ties. Oftentimes, company ownership is distributed not share personal data due to privacy regulations. Note over family members to obfuscate the actual ownership that this lack of ground truth data also severely limits the structure leading to issues as in the example illustrated applicability of popular Machine Learning techniques for in Figure 1. related problems like Knowledge Graph embedding.

Consequently, if we detect a family link between a In this paper, we present novel in-progress work on person and a person that respectively own a com- combining similarity measures that indicate potential family links with new methods for many-valued reasoning over uncertain data in KGs to obtain a unified picture of potential family links in the Enterprise Knowledge Graph of Italian companies.

In a first step, we infer connections between persons based on the information pertaining to company ownership and the available anagraphic data, such as addresses and names of company owners. For example, given perPublished in the Workshop Proceedings of the EDBT/ICDT 2022 Joint Conference (March 29-April 1, 2022), Edinburgh, UK $ [e-mail] (M. Lanzinger); [e-mail] (S. Sferrazza)

0000-0002-7601-3727 (M. Lanzinger); 0000-0001-9569-4428 (S. Sferrazza)

© 2022 Copyright for this paper by its authors. Use permitted under Creative CPWrEooUrckReshdoinpgs IhStpN:/c1e6u1r3-w-0s.o7r3g CCoEmmUoRns LWiceonsrekAstthribouptionP4r.0oIncteerenadtiionnagl s(CC(CBYE4U.0)R.-WS.org) sons and with the same surname, both having a derived extensional component that can be produced as shares in the same companies and living in the same the result of the application of the inference rules over region, we may reasonably infer a family link between the ground extensional component (with the so-called them. This hypothesis is strengthened by the knowledge “reasoning” process). of the Italian economic system, where a large number of Our target is the Enterprise Knowledge Graph of Italcompanies have families as their major shareholders. We ian companies, containing the most updated data at our extend such inference beyond exact matches of data, e.g., disposal. We focus on non-listed companies. For each if and in the scenario above lived in neighbouring of them, the graph contains several features including regions rather than the same region the inference could legal name, registered ofice address, incorporation date, still be argued, although with less certainty. legal form, shareholders. A shareholder can be either

At the same time, family links observe several common a company or a person, with the standard anagraphic logical properties, such as transitivity or symmetry, that information. Shares can be associated with diferent legal can be used to detect further family links through logical rights (e.g., ownership, bare ownership, etc.). We focus reasoning. However, since the similarity metrics produce on all forms of ownership and include in the KG compauncertain observations, the use of classical logical reason- nies having at least one shareholder. The graph counts ing (which is limited to statements that are either fully 11.97M nodes, representing the shareholders, and 14.18M true or false) is severely limited in this setting. Rather edges denoting share ownership. than reducing our uncertain observations to true/false via thresholds or similar techniques, we propose the use of MV-Datalog± [ 7 ], a recent extension of Datalog± [ 8 ] 3. Extracting Uncertain Family with many-valued semantics. Many-valued here refers Links to the use of degrees of truth, which we use to model uncertainty, rather than the classical paradigm of every In this section, we describe our technique for extracting fact being either absolutely true or false. MV-Datalog± uncertain family links from the Italian companies KG. allows us to combine the uncertain observations with log- Considering the complex analysis that we aim to perform, ical reasoning and certain knowledge, such as a company taking into account all the person nodes in the graph ownership KG, expert knowledge, or known relation- would lead to the intractability of the uncertain reasoning ships, in a single framework. inference. Furthermore, most of the nodes would not be

In the following, we discuss how these two compo- relevant for the scope of our analysis. Thus, spending nents can interact to provide a powerful reasoning system computational time over those would not be wise. The for detecting family links in the Enterprise Knowledge ifrst objective is to reduce the search space in such a way Graph for Italian companies. While the presentation fo- that it is likely a family connection exists each time two cuses on this specific setting, we believe that our methods person nodes are compared. can be widely applicable and that uncertain reasoning Our approach is based on the following assumption: peosystems open up a variety of new opportunities for the ple owning a similar amount of shares across the same use of KGs. Details of the problem setting and the de- companies tend to have family connections. According rived observations of possible links between persons are to these remarks, we consider the following three-step presented in Sections 2 and 3, respectively. We discuss process in order to extract family links having a degree the interaction with MV-Datalog± for unifying and ex- of uncertainty. The first two steps aim at reducing the tending uncertain observations in Section 4. Results of search space through partitioning techniques. In the last preliminary experiments are discussed in Section 5. We step, each pair of nodes in the reduced space is compared conclude with an outlook of planned next steps in Sec- to evaluate three diferent similarity scores. The higher tion 6. the scores, the more likely the family connection. (i) The first step involves the computation of weakly connected components (WCCs) by exploiting a more com2. The Enterprise Knowledge plex concept of the traditional ownership that is called Graph of Italian Companies integrated ownership. This is a notion of accumulated ownership from a company to a company : it acA Knowledge Graph (KG) is a semi-structured data model [ 9 ]counts for the ownership that retains of along composed of three components: (i) a ground extensional direct and indirect connections. In terms of the flow of component (or simply extensional component), that is, a dividends, integrated ownership can be seen as the cumuset of relational constructs for schema and data, which lative flow from to , justified by direct and indirect can be efectively modelled as a property graph; (ii) an shareholding [ 5 ]. intensional component, that is, a set of inference rules over The graph consists of about 21 million connections based the constructs of the ground extensional component; (iii) on the integrated ownership. This amount of relations takes into account both direct and indirect links. The number of connections is significantly cut by removing the ones characterized by an integrated ownership value < 0.001. At this point, some of the nodes are no longer linked to any other node in the graph due to the removal of related edges.

This diminished graph presents about 1,3 million WCCs, in average composed by a number of nodes between 3 and 10, see Figure 21, while the largest WCC has more than 1,5 million nodes. All the WCCs composed by a single node have not been further considered. According to the WCC properties, a node is only reachable from the nodes within the same component. This feature fully satisfies our previous assumption, since two persons could have a family link only if at least one connection (direct or indirect) through their companies exists.

(iii) In step 3, all the pairs of nodes possibly having a family connection, i.e. all the nodes within the same cluster, are compared to evaluate the similarity scores.

The final set of candidates is composed of approximately 41 million pairs.

The similarity score based on the amount of shares across the same companies is computed as follows: = ∑︀

+ ∈(∩) ∑︀ ∈ +

∑︀ ∈

(1)

1For the sake of visualization the communities with the higher

number of nodes and density next to 0 have been omitted = 0.77 = 0.37 = 0.46

We can notice that the score increases when there is a experts to introduce their knowledge in the reasoning concentration of interests over the same companies. In- process. Finally, extensive research in the field has also deed, while and ownership revolves around , identified methods and fragments that allow for highly has a relevant share of another company, . This brings eficient reasoning in these languages (e.g., [ 12, 13 ]). to lower scores associated with , and, in particular, This confluence of desirable properties has led to a re,. cent surge in the use of Datalog and its derived languages in complex Data Analysis tasks [ 14 ]. Here we make use

The second score takes into account the string similar- of a very recent such extension named MV-Datalog± ity between the living addresses. Given two persons [ 7 ], which extends Datalog± to many-valued (or fuzzy) and having address and , the semantics. That is, instead of the classical dichotomy similarity score is given by the Levenshtein distance [ 10 ] between true and false facts, one considers degrees of as follows: truth, expressed as rational numbers in the interval [ 0, 1 ] (cf., [ 15 ]). Many-valued logical semantics are interesting = ℎ( , ) in practice since degrees of truth can be used to naturally (2) express vagueness or uncertainty that often occurs in real

world data analysis tasks. Moreover, important benefits

Finally the third score evaluates the proximity of the of rule-based reasoning, such as transparency and exaddress postal code, derived from the living address at- plainability, are preserved when moving to many-valued tribute, as: semantics. For space reasons, we can not recall the semantics of MV-Datalog± in detail here. Intuitively, rules = (3) amroedienltesurpcrhetthedatansoinatŁoumkacsainewb eiclzeslosgtricueanadndweevfinerdytrhuele Where represents the number of the first common digits is satisfied to some given truth degree. Such minimal shared by the two postal codes and is the postal code fuzzy models are in fact unique and can be computed in length. For instance, the postal codes 00100 and 00198 polynomial time in data complexity when there is exitenhave the first three digits in common ( k = 3 , n = 5 ) and tial quantification in the head of rules. With existential the resulting similarity is 0.6. quantification, current results [ 7 ] are restricted to cases

The result of the process is summarized in the follow- where the oblivious chase is finite. However, in practice, ing table: utilization of termination strategies for chase sequences – e.g., as used for guarded or warded Datalog± [ 12 ] – 1 2 ... 12 12 12 can allow for good approximation of minimal -fuzzy models in settings where the plain oblivious chase may a b ... 0.77 0.6 0.7 not terminate. a c ... 0.37 0.5 0.8 In the application presented in this paper, we use MVb c ... 0.46 0.1 0 Datalog± to reason over the uncertain observations deTable 1 scribed in Section 3. Here we highlight some key ways Similarity scores table in which natural constructs in MV-Datalog± implement important behaviour in our family link inference system.

Note that the following examples have been simplified for the sake of presentation and that a full system can consider much more complex constructs.

4. Uncertain Reasoning with

MV-Datalog±

Combining Multiple Sources of Uncertainty As discussed in the previous section, we start from some diferDatalog and its more recent extension Datalog± are popu- ent vague observations on similarities between persons. lar formal languages for rule-based reasoning. They com- Ultimately we want to combine these observations into a bine high expressiveness with several important prop- single judgement of how certain we are wrt the eventual erties for use in practice. In particular, they allow for family link between two people. By using MV-Datalog± eficient reasoning and explainable answers despite be- we express how to combine these diferent sources of ing expressive enough to capture a number of popular vague observations simply through the logical relationformalisms, such as the OWL 2 QL and OWL 2 EL profiles ships of the observations. Note that in this case these of the OWL 2 for semantic web reasoning, or popular connections are direct representations of expert knowldescription logics like DL-Liteℛ or ℰ L [ 11 ]. At the same edge but can also be derived from other sources, e.g., laws time, rule-based languages are designed to be easily un- and regulations. For example, from our hypothesis, we derstandable and writable by humans, allowing domain believe that two people who own the same amount of shares in the same company (the own score interpreted as a fuzzy predicate from Section 3), and who live in the same region are related. Using MV-Datalog± we can express this directly through the simple rule for the vague observations own and postal as described above. form as we would in any Datalog program for certain knowledge: related (, ) ← related (, ) ← related (, ). related (, ), related (, ). related (, ) ← own(, ), postal (, ). Explainability and Transparency In a regulatory context, it is critical to know why a system infers family Importantly, if the region and ownership structure of two links. Many popular Machine Learning methods struggle people is exactly the same, i.e., the respective own and to provide such explainability and transparency at the postal observations are completely true (truth degree 1), required level. By inferring family links through logical then the relatedness of the respective persons will be reasoning, our system is fully transparent and can proinferred as completely true. If one or both of the observa- vide full explanations, consisting of the individual steps tions are uncertain, the truth degree of related (, ) of deduction that ultimately led to a link being inferred. is derived through more complex means in a way that is Consider a link between A and B that has been inferred consistent also with all the other rules. with truth degree (i.e., level of certainty) 0.78 as a simple

In a similar fashion, we infer parent/child relationships example with explanation (in formal terms): for persons living at the same address where one person is much younger than the other. Again rule-based rea- child (A, C ) ← age_gap(A, C ), addr (A, C ) soning makes it simple to specify such a rule, but also related (A, C ) ← child (A, C ) to express that the child relationship is a special case of related (C , B ) ← own(C , B ), postal (C , B ) related : related (A, B ) ← related (A, C ), related (C , B ) child (, ) ← age_gap(, ), addr (, ). where the observation postal (C , B ) has truth degree related (, ) ← child (, ). 0.8, and addr (A, C ) is 0.98 true, and all other input observations are certain (truth degree 1). A natural reading This also illustrates how the vague observation addr can of the explanation is that we deduce (with certainty 0.98) imply relatedness in a significantly diferent way than that A is a child of C, making them related with the same own or postal. The final solution model for the related certainty. In this simple example, C and B have the exrelation is then derived from all of these logical relation- act same company ownership and live in very similar ships and interactions globally through the program to regions, hence we deduce they are related with truth provide a unified answer that is consistent with the input degree 0.8. By transitivity of relatedness, this then also observations and the specified logical rules. Furthermore, implies that A and B must be related and by the semanit is possible to specify weights for rules to express their tics of MV-Datalog± 2 the resulting fact related (A, B ) importance relative to one another and can further afect has truth 0.78. Note that the truth degree is generally the solution of MV-Datalog± inference. not derived by simple forward propagation but requires more complex considerations since diferent paths of Fuzzy Closure over Logical Properties Family re- rule application can lead to the same consequences (say lations follow some logical axioms such as symmetry A and B also had some common ownership). For a formal or transitivity. Naturally, if we detect that persons definition of the semantics of MV-Datalog ± we refer and are related, as well as and , we can deduce to Lanzinger et al. [ 7 ]. that also and are related. In rule-based reasoning, all such implied connections can be easily deduced Advanced Data Cleaning MV-Datalog± also allows by expressing the respective properties in logical terms. for constraints, that is rules with falsum ⊥ in their head With uncertain information such situations become more which express that the body of the rule shall not be satiscomplex, say we deduce related (, ) with truth 0.7 ifed. In a many-valued context, such constraints can be a and, independently, related (, ) with truth 0.9, then valuable tool for data cleaning according to the logical it can be unclear how to consolidate this when assum- properties of the domain. For example, if we are worried ing that related is symmetric. Enforcing such properties about data inaccuracies leading to two persons being invia ad-hoc computation is often highly challenging es- ferred as children of each other, we can express that this pecially when trying to reconcile multiple properties at is impossible through the following constraint: the same time (such as symmetry and transitivity). MVDatalog± ofers natural semantics for such situations ⊥ ← child (, ), ℎ(, ) in which it will produce the equilibrium where every 2In this simple example this works out to the Łukasiewicz trule is as satisfied as possible. This allows us to express norm Truth( ⊙ ) = max{0, Truth( ) + Truth( ) − 1} these important properties in simply their natural logical of the two body atoms and .

Constraints semantically behave like all other rules in sentative of many real instances4. We can conclude that our many-valued setting in that the solution model is the the computational efort required of our system is low model that globally satisfies all rules as much as possible, enough for our setting and we expect this to still hold which implies violating all constraints as little as possible. when further complexity is introduced (see Section 6). Again weighting also allows us to specify the relative We also expect significant further improvements of these importance of each constraint. runtimes with further development of the MV-Datalog± reasoner, which itself is in an early stage of development.

Interaction with Classical Knowledge Bases As a With respect to the resulting related relation. We infer ifnal point, since MV-Datalog ± is an extension of plain almost 1000 tuples for the relation in the small instance Datalog, it is also well suited for tasks where we want (this includes the tuples resulting from transitive and to combine reasoning over vague inputs with classical symmetric closure), with varying degrees of truth. Simiknowledge bases. It would, for example, be natural to larly, we infer a related relation containing about 9000 extend our system with various kinds of social graphs. tuples for the medium-sized instance. Manual inspecInteraction with such classical (non-vague) knowledge tion of results and respective explanations confirm that bases requires no special interfaces since MV-Datalog± the tuples and their inferred degree of truth match the behaves exactly like plain Datalog on rules where the intentions of domain experts that proposed the rules, inputs are not vague (i.e., have truth 0 or 1). confirming the efectiveness of our proposed approach.

5. Preliminary Experiments

6. Conclusion and Outlook

Here we briefly report on early experiments with a proof- In this paper, we considered the family link detection of-concept system built following the ideas described problem in the setting of the Italian companies knowlabove in Sections 3 and 4. We compute fuzzy relations edge graph, described in Section 2. We present a novel own, addr, and postal following the methods and cluster- proof-of-concept system based on uncertain predictions ing described in Section 3. Additionally, we consider a of family links, paired with advanced fuzzy reasoning. (not fuzzy) relation age_gap to specify whether an age gap We use graph-theoretic techniques to reduce the search between two persons is large enough for a parent/child space significantly and then compute a number of fuzzy relationship. Using these relations as input we use an relations that may indicate family links between perearly implementation of a MV-Datalog± reasoner, built sons. We discuss how fuzzy reasoning in MV-Datalog± on top of the state-of-the-art KGMS Vadalog [ 16 ] as well provides a powerful framework for reasoning on such as the mathematical optimization solver Gurobi [ 17 ], to relations as an alternative to popular Machine Learning infer a fuzzy related relation (including explanations for methods, especially in settings with little to no training every inferred fact) from rules that implement the main data. Early experiments suggest that this approach can ideas shown in Section 4, including transitive and sym- produce efective systems and in particular so in regulametric closure and multi-layered combination of diferent tory applications where transparency and explainability fuzzy observations3. are highly valuable.

Our preliminary experiments followed two main goals. The presented system design provides high flexibilUnderstanding whether the reasoning in MV-Datalog± ity in further development. Further data sources can be is feasible in acceptable time for our setting and how the introduced naturally as further input relations with no inferred relationships match the intuition and intention additional efort. Adapting and adding rules is a straightof our rules. forward task that can be performed at any time by domain

With respect to the performance, we ran tests with a experts. small and a medium-sized dataset, with each aforemen- One particular promising next step is the introduction tioned relation containing 1000 or 10000 tuples, respec- of geocoding in addition to the computation of the score tively. On a standard consumer laptop (8GB Memory, 1.4 similarity , . Geocoding overcomes certain limGHz Quad-Core Intel Core i5), inference of the related its of traditional methods based on string similarity. Inrelation (as well as all corresponding explanations) takes deed, it is able to reflect the real proximity of addresses roughly 10 seconds for the small instance and about 160 according to their geographical coordinates. This adseconds for the medium-sized test dataset. Note that due dition can make our inference based on location much to the efective partitioning of the search space through more robust, especially when we have two geographically the combined use of WCCs and surname clusters as out- close addresses with a total diverse nomenclature and in lined in Section 3, these instance sizes are already repre

3Integration of additional classical knowledge bases was not

part of the tested program

4Reasoning needs to only be performed on single clusters in

WCCs independently of other clusters and WCCs. the case where addresses present severe transliteration errors.

Further planned extensions include the integration with additional knowledge graphs containing certain knowledge and in particular social graphs. The complex integration of various sources of certain knowledge with fuzzy observations will allow us to model family links in a more detailed way and produce more accurate inferred related relations.

Finally, the current work focuses on comparisons beyond people with the same surnames. Future work will aim to identify possible links with diferent surnames while retaining the computational benefits of the clustering as far as possible.

Acknowledgments

Stefano Sferrazza was supported by the Austrian Science Fund (FWF):P30930. Matthias Lanzinger acknowledges support by the Royal Society “RAISON DATA” project (Reference No. RP\R1\201074).

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