=Paper=
{{Paper
|id=Vol-2644/paper41
|storemode=property
|title=Reasoning on Company Takeovers during the COVID-19 Crisis with Knowledge Graphs
|pdfUrl=https://ceur-ws.org/Vol-2644/paper41.pdf
|volume=Vol-2644
|authors=Luigi Bellomarini,Marco Benedetti,Stefano Ceri,Andrea Gentili,Rosario Laurendi,Davide Magnanimi,Markus Nissl,Emanuel Sallinger
|dblpUrl=https://dblp.org/rec/conf/ruleml/BellomariniBCGL20
}}
==Reasoning on Company Takeovers during the COVID-19 Crisis with Knowledge Graphs==
https://ceur-ws.org/Vol-2644/paper41.pdf
Reasoning on Company Takeovers during the
COVID-19 Crisis with Knowledge Graphs∗
Luigi Bellomarini1 , Marco Benedetti1 , Stefano Ceri2 , Andrea Gentili1 ,
Rosario Laurendi1 , Davide Magnanimi1,2 , Markus Nissl3 , and
Emanuel Sallinger3,4
1 Banca d’Italia
2 Politecnico di Milano
3 TU Wien
4 University of Oxford
Abstract. When some country takes a disproportionate hit by a large-
scale turmoil—just like Italy did during the COVID-19 pandemics—the
share prices of its companies plunge. Suddenly, it becomes feasible to
attempt foreign takeovers of national assets, including those of strate-
gic interest. To avert this risk, the Government can veto transactions by
summoning the so-called “Golden Powers”. Or, it can work to proactively
identify structural weaknesses in the control or shareholding chains of key
companies, in order to reinforce them without resorting to special pow-
ers. Sometimes, vulnerabilities and attacks hide in plain sight due to how
complex and intertwined the network of mutual company shareholding
is. In this work, we show how to leverage Knowledge Graphs (KGs) as
a representation and reasoning framework to analyze both reactive and
proactive measures against takeover attempts, however intricate the set-
ting where they take place. We formally characterize a set of reasoning
tasks that define when and if to employ Golden Powers, plus others that
aim at pinpointing companies prone to attacks. These criteria are exer-
cised on the real network of all Italian companies, built for the occasion.
A rich set of experiments is provided, including on several large synthetic
instances, to prove the robustness of our method.
Keywords: Knowledge Graphs · Reasoning · Company Takeovers.
1 Introduction
The COVID-19 outbreak has had an immense impact on our society. Besides the
critical health crisis, it has become clear that preventing, or at least managing,
its large-scale economic effects will become critical as well. The work we present
here deals with reasoning about company takeovers. To this end, we employ
Knowledge Graphs (KGs) as a representation and reasoning framework: Our
approach analyzes automatically a large graph of knowledge (representing the
∗ Theviews and opinions expressed in this paper are those of the authors
and do not necessarily reflect the official policy or position of Banca d’Italia.
Copyright c 2020 for this paper by its authors. Use permitted under Creative Com-
mons License Attribution 4.0 International (CC BY 4.0).
entire set of Italian companies and their mutual financial relationships) in search
for ongoing or potential hostile takeovers over companies of strategic national
interest. Specific reactive or proactive defence measures by the Government, pos-
sibly involving the use of the so-called “Golden Powers” (GPs), are automatically
produced as a result of our analysis. This initiative forms one pillar of a flag-
ship project launched by the Central Bank of Italy in reaction to the COVID-19
crisis,5 and is in line with a call to action by the President of the European
Commission6 on counteracting hostile takeovers of strategic companies.
It is essential that the ownership of — or, more importantly, the control upon
— companies deemed of strategic relevance (e.g., in the energy, military, trans-
port, telecommunications sectors) remains in the hands of trusted shareholders.
Yet, with the COVID-19 outbreak, companies stretched by massive shutdowns
and production plunge are subject to an abnormal number of hostile takeover
attempts because, in conditions of market turbulence, attackers try to take ad-
vantage of lowered share prices. A hostile takeover consists in gaining the control
of a target company against the will of its management. Company control can
be gained directly by acquiring the majority of the target company shares, or
indirectly, by gaining control over a set of companies that jointly own the ma-
jority of the shares of the target. In real-world company networks, such indirect
undertakings with very long and intertwined control chains are regularly present.
Multiple countries have historically resorted to legal frameworks to protect
strategic companies against foreign takeovers [16]. Italy is a relevant example:
Being one of the countries most struck by the COVID emergency, it carried out a
careful application of the so-called Golden Powers [19], that is, the possibility for
the central Government to veto individual acquisition transactions (e.g., in terms
of shares of stocks) that would cause strategic assets to fall victim to takeovers.
Likewise, the Government can intervene to secure companies by acquiring or
increasing its participation in the strategic firms (technically, investment beef-
up) via publicly controlled intermediaries.
Golden Power Settings. Unfortunately, an effective application of the men-
tioned legal frameworks (and of GPs in particular) is by no means trivial. How
can we tell whether a transaction is a takeover attempt? Will a transaction
lead to a takeover? What is the minimum amount of share that must shift to
public control in order to protect a company? And, how to protect against co-
ordinated, collusive, transactions aiming at a takeover? These problems lend
themselves to be addressed by a declarative and fully explainable approach, and
encoded as reasoning tasks on the KG of the Italian companies, built and main-
tained by the Bank of Italy [2]. The technical challenges are significant: Dealing
with indirect control chains requires a Knowledge Representation and Reasoning
(KRR) language that supports recursion and creation of new values. Indeed, the
problems underlying the application of GPs are hardly addressed by traditional
data management technology, where support for recursion is absent or laborious.
Moreover, the massive amount of domain knowledge available makes resorting
to a pure graph database impractical, as it leads to either proliferation of over-
5 https://kg19.bankit.art
6 https://trade.ec.europa.eu/doclib/press/index.cfm?id=2124
complicated non-scalable queries or to a substantial impossibility of representing
the necessary queries within poorly expressive host languages. Finally, machine
learning or network analysis approaches would lack explainability.
KG19. This work leverages our experience in state-of-the-art reasoning in Vada-
log KGs [6,7] to study the impact of the outbreak on the Italian company
network under various perspectives and provide policymakers, analysts, and
economists, with actionable AI tools and data to support businesses and lessen
the economic impact of COVID-19. Although we focus on the Italian case, our
initiative aims at providing methodologies and tools that are valid in general,
independently of the specific country and crisis situation. A wider picture of the
lockdown impact on the company network can be found in a recent report [5].
Contribution and Overview. We present the first results of the application
of rule-based reasoning on KGs to aid decision making about the application of
Golden Powers to contrast hostile takeovers. In particular, this paper contributes:
– The main references to Vadalog (Section 2) and a compact formalization of
the company control problem (Section 3) as background material.
– A formal characterization and discussion of a set of reasoning tasks about
Golden Powers (Section 4), modeling the possibility of different Governments
to intervene on transactions that may underlie takeover attempts.
– A discussion of the application of our techniques to the real data from the KG
of the Italian companies, with an evaluation of the soundness of the approach
for real takeover patterns. We also study the scalability of the approach on real
data as well as on synthetic instances of the relevant GP reasoning tasks and
of the company control problem in the Vadalog System (Section 5).
Related work is discussed in Section 6, while Section 7 concludes the paper.
2 Vadalog Knowledge Graphs
The formalization of the company control problem and the GP settings in this
paper are encoded in Vadalog, a language from the Datalog± family [9,13];
experimental evaluations are run in the Vadalog System. Datalog± generalizes
Datalog with existential quantification in the rule conclusion. A rule is a first-
order sentence of the form ∀¯ 𝑥∀¯𝑦 (𝜑(¯
𝑥 , 𝑦¯) → ∃¯𝑧 𝜓(¯
𝑥 , ¯𝑧)), where 𝜑 (the body) and 𝜓
(the head) are conjunctions of atoms. For brevity, we omit universal quantifiers
and denote conjunction by comma. As usual in this context, the semantics of a
set of rules is defined by the well-known chase procedure. The core of Vadalog
is based on Warded Datalog± [6], a syntactic restriction to Datalog± that guar-
antees decidability and tractability in the presence of recursion and existential
quantification. In terms of expressive power, Warded Datalog± captures full Dat-
alog and OWL 2 direct semantics entailment regime for OWL 2 QL. The language
underpinnings are exploited by the reasoner to allow for efficient execution of
reasoning tasks [7]. Vadalog augments Warded Datalog± with supplementary
features such as aggregation, algebraic operations, and stratified negation.
Vadalog supports monotonic aggregations, whose full details can be found
in [7]. However, a simpler form of aggregation, which suffices to our ends, is
A 0.3
0.8 0.2
E
C C
0.21
A D A D 0.05
0.2
0.7 0.1
0.30 0.31
0.2 0.39 0.55 D
0.46
0.11
0.2
B B C B
(a) (b) (c)
Fig. 1: Sample ownership graphs where 𝐴 controls 𝐵. Nodes are entities; solid
edges are direct ownerships; dashed edges are control relationships.
based on stratified semantics, where the basic idea for our case is very simple:
An aggregation function (e.g., sum, in Section 4) is computed only when its input
operands are completely known. All our use cases admit such simplification.
3 Company Control Problem: A Deductive Approach
Underlying the study of hostile takeovers is the notion of company control. It
concerns decision power, i.e., when a company can direct the decisions of an-
other company by controlling the vote majority via the majority of the shares.
Let us consider an ownership graph, i.e., the directed graph where nodes are
shareholders and edges represent share ownership.
Along the lines of existing formulations from the logic and database litera-
ture [10], we see the company control problem as follows.
A company 𝑥 controls a company 𝑦, if: (i) 𝑥 directly owns more than 50% of 𝑦;
or, (ii) 𝑥 controls a set of companies that jointly (i.e., summing their shares),
and possibly together with 𝑥, own more than 50% of 𝑦.
Figure 1 shows basic cases of company control. In Figure 1(a), the first clause
applies: Company 𝐴 directly controls company 𝐵. In Figure 1(b), the second
clause applies: Company 𝐴 does not directly control 𝐵; nevertheless, it has an
80% share on company 𝐶 and hence it controls 𝐶. Thus, the total share of
company 𝐵 that 𝐴 controls rises to 61%, which is the sum of the direct 30%
ownership of 𝐴 on 𝐵 and the 31% ownership of the controlled company 𝐶 on 𝐵.
In the end, 𝐴 controls 𝐵. Figure 1(c) demonstrates a more convoluted form of
control: An entity 𝐴 can control a company 𝐵 anywhere in the graph, given that
𝐴 can indirectly control the majority of the shares of 𝐵 even if no direct control
exists between 𝐴 and 𝐵 or even between any intermediate company and 𝐵.
Company control can be formulated as a Vadalog reasoning task:
Company(𝑥) → Control(𝑥, 𝑥) (1)
Control(𝑥, 𝑦), Own(𝑦, 𝑧, 𝑤), 𝑣 = sum(𝑤), 𝑣 > 0.5 → Control(𝑥, 𝑧) (2)
Assuming that every company has control on itself (Rule 1),7 we inductively
define control of 𝑥 on 𝑧 by summing the shares of 𝑧 owned by any company
𝑦 over all companies 𝑦 controlled by 𝑥 (Rule 2). The presence of cycles in the
ownership graphs, a common case indeed, is irrelevant for control purposes.
7 This formalization of the base case is slightly different from the natural definition
but commonly assumed in the literature as it is more compact and formally equivalent.
4 Reasoning on Golden Power
In this section we elaborate on a set of KG-based applications revolving around
the use of GPs. The framework we develop covers five fundamental concerns
raised by business stakeholders, related to: Decision and policy making, advice
to be given to companies, and proactive actions to be taken. We present a number
of core reasoning tasks providing insights on: 1. detecting cases of transactions
hiding possible takeover attempts; 2. suggesting limits within which GPs may be
exercised; 3. giving options for proactively protecting companies from takeover
attempts. Figure 2 summarizes the scenarios under consideration. Each column
describes one scenario, specifying its goal, general setting, business question, and
resulting insight. At the bottom of each column, we report one example.
At the core of our cases, there is the Company Control setting from Sec-
tion 3. Companies are assigned different roles: trusted (e.g., public companies or
Governmental bodies, pink in the figure), attacker (e.g., a company out of the
national border in the figure, i.e., incorporated or organized under the law of
another country), or target (e.g., the strategic company to be protected, green);
all the others are assumed to be neutral (gray).
We perform both reactive analysis, checking whether specific variations to the
graph generated by candidate transactions (acquisition of shares) culminate in
unwanted takeovers, and proactive analysis, detecting structural vulnerabilities
and possible countermeasures, independently of any possibly ongoing attack.
In the following paragraphs, we introduce the Vadalog formulations of the
five cases. Each one is an extension of Company Control, so Rules 1 and 2 from
Section 3 are assumed to be inherited by all the formulations. Attackers, target,
and trusted companies are respectively denoted by atoms V, T, and P.
Encoding these criteria as rules in an expressive and scalable declarative
framework such as Vadalog is of the essence here because while we have an-
alyzed the key reasoning patterns in this work, more emerge on a daily basis
during the interactions with business experts: Changes that would radically im-
pact a procedural approach (requiring a substantial rewrite) are just a minor
amendment away when the domain knowledge is captured declaratively. Not
only does Vadalog allow us to quickly test and deploy new criteria, but the
amount of time we spend to get sure we are on the same page as our business col-
leagues — i.e., to convince them that the implementation is actually computing
what we have agreed on paper — dramatically shortens.
Golden Power Check. We show how to detect individual transactions that
cause some target company to be taken over. This is a case where Golden Power
may be an option to exercise. We call this problem: Golden Power Check.
Example. Let us consider the example shown at the bottom of Figure 2(1). We
first consider the setting. Company 1 is in the set of attackers, e.g., potentially
attacking companies under investigation (forming the set 𝑉 in the definition
shown in Figure 2), while the colored node 𝐵 is in the set of target companies
(forming the set 𝑇 in our definition shown in Figure 2).
Candidate transactions are shown using dashed edges. Our first candidate
transaction is 𝑡 1 , where an ownership of 51% of 𝐴 is acquired by 1. The second
candidate transaction is 𝑡2 where an ownership of 90% of 𝐶 is acquired by 𝐵. Let
Fig. 2: Golden Power Settings
(1) Golden Power (2) Golden Power (3) Golden Power (4) Collusion Golden (5) Cautious Golden
Check Limit Protection Power Check Power Check
Analysis: Reactive Analysis: Proactive Analysis: Proactive Analysis: Proactive Analysis: Reactive
Goal: Checking whether Goal: Computing the Goal: Computing the Goal: Checking whether Goal: Checking whether
an acquisition (of shares, maximum amount of share increment needed an acquisition (of shares, an acquisition (of shares,
stocks, etc.) causes any share a company 𝑥 can by trusted compa- stocks, etc.) causes any stocks, etc.) causes any
target company to be- buy of a company 𝑦 nies to prevent hostile target company to be target company to be-
come controlled by an at- without controlling any takeovers. possibly controlled by a come possibly controlled
tacking company. company in a set 𝑇. Setting: Let 𝑇 be a set set of attacking compa- by an attacking com-
Setting: Let 𝑇 be a set Setting: Let 𝑇 be a set of target companies and nies acting in collusion. pany for which share-
of target companies, 𝑉 a of target companies and 𝑉 be a set of attacking Setting: Let 𝑇 be a set holding information is
set of attacking compa- 𝑉 be a set of attacking companies. Let 𝑃 be a of target companies, 𝑉 be incomplete.
nies, and 𝑁 a set of neu- companies. Let 𝑡 be a set of trusted companies a set of attacking compa- Setting: Let 𝑇 be a set
tral companies. Let 𝑡 be transaction (e.g., an of- (such that 𝑃 is disjoint nies, and 𝑁 a set of neu- of target companies, 𝑉 be
a transaction (e.g., an of- fer issued by a company from 𝑉 and 𝑇). tral companies. Let 𝑡 be a set of attacking compa-
fer issued by a company 𝑥 to buy an amount 𝑠 of Question: Which acqui- a transaction (e.g., an of- nies, and 𝑁 a set of neu-
𝑥 to buy an amount 𝑠 of shares of a company 𝑦), sitions of shares of com- fer issued by a company tral companies. Let 𝑡 be
shares of a company 𝑦), with 𝑥 ∈ 𝑉, 𝑦 ∈ 𝑇. panies in 𝑇 by compa- 𝑥 to buy an amount 𝑠 of a transaction (e.g., an of-
with 𝑥 ∈ 𝑉, 𝑦 ∈ 𝑇 ∪ 𝑁. Question: What is the nies in 𝑃 guarantee that shares of a company 𝑦), fer issued by a company
Question: Does 𝑡 cause maximum value 𝑠 𝑚𝑎𝑥 for no set of transactions 𝑡 with 𝑥 ∈ 𝑉, 𝑦 ∈ 𝑇 ∪ 𝑁. 𝑥 to buy an amount 𝑠 of
any company in 𝑉 to gain 𝑠 such that there are no (from 𝑥 to 𝑦, with 𝑥 ∈ 𝑉, Question: Does 𝑡 cause shares of a company 𝑦),
control of any company companies in 𝑉 that gain 𝑦 ∈ 𝑇) allows any com- 𝑉 to gain joint control of with 𝑥 ∈ 𝑉, 𝑦 ∈ 𝑇 ∪ 𝑁.
in 𝑇? control over any com- pany in 𝑉 to gain control any company in 𝑇? Question: Assuming
Insight: If the answer is pany in 𝑇? over one in 𝑇? Insight: If the answer is that any unassigned
YES, consider the pos- Insight: Transactions Insight: Consider the YES, consider the pos- share of 𝑦 is in fact
sibility to block 𝑡 via that acquire (much) possibility to (temporar- sibility to block 𝑡 via owned by some 𝑣 ∈ 𝑉,
Golden Powers. less than 𝑠 𝑚𝑎𝑥 shares ily) buy shares of 𝑇 via 𝑃 Golden Powers. does 𝑡 allow 𝑣 to gain
of 𝑦 do not require the as per the answer to the control of 𝑦?
application of Golden above question to pre- Insight: If the answer is
Powers immediately to vent takeovers (Golden YES, consider the pos-
protect 𝑦. Powers are not needed). sibility to block 𝑡 via
Golden Powers.
1 1 2 1
0.9 C 0.9 C 0.9 C 0.9 C
1
Abroad
Abroad
Abroad
Abroad
x 0.2
0.31 0.31 0.31
y
y
y
y
0.51 0.75 0.51
ar
ar
ar
ar
nd
nd
nd
nd
0.51
ou
ou
ou
ou
b
b
b
b
al
al
al
al
ion
ion
ion
ion
0.2 0.2 0.2 0.2
A A A A
Nat
Nat
Nat
Italy Italy Italy
Nat
B B B Italy B
us first consider transaction 𝑡 1 as our transaction of interest. This would give
1 control of 𝐴, and hence a 20% ownership of 𝐵. So far, the total ownership of
target company 𝐵 by company 1 is thus 20% with no need to block 𝑡1 .
Now assume that transaction 𝑡1 was processed (i.e., it becomes a solid line),
and consider transaction 𝑡2 , where an ownership of 90% of 𝐶 is obtained by 1.
This would give 1 control of 𝐶 and hence 31% ownership of 𝐵. Together with
the ownership of 20% of target company 𝐵 that 1 already holds, it now has 51%
ownership of company 𝐵 and thus controls it. Transaction 𝑡 2 must be blocked
using Golden Power if the target company 𝐵 should not come under the control
of 1. Finally, we remark that had transaction 𝑡 2 come before 𝑡 1 , it would have
been fine to process 𝑡2 and block 𝑡1 . This concludes our example.
This line of reasoning can be formalized as a Vadalog reasoning task by
extending Company Control with the following rules:
V(𝑥), ¬V(𝑦), Tx(𝑥, 𝑦, 𝑤) → Own(𝑥, 𝑦, 𝑤) (1)
V(𝑥), T(𝑦), Control(𝑥, 𝑦) → GPCheck(𝑥, 𝑦) (2)
Rule 1 defines that, for the purpose of our analysis, we consider transaction 𝑇𝑥
to be virtually applied, i.e., leading to actual ownership even if it has not taken
place. Then, Rule 2 captures our goal by computing all companies in 𝑉 that
control at least one company in 𝑇. If GPCheck is empty, there is no reason to
use Golden Powers. In case it is non-empty, it gives a list of the companies which
are possible subject of takeovers caused by the single acquisition of share 𝑇𝑥.
Golden Power Limit. The second relevant problem is to advise companies
about what transactions are allowed to take place (without requiring the use
of GPs to prevent a takeover). We call this problem Golden Power Limit. The
definition and an example are given in Figure 2(2). A full explanation of this
(and following) examples can be found in the appendix,8 while the definition can
be formulated with the following Vadalog rules:
Control(𝑥, 𝑦), Own(𝑦, 𝑧, 𝑤), 𝑣 = sum(𝑤) → PControl(𝑥, 𝑧, 𝑣) (1)
V(𝑥), T(𝑦), PControl(𝑥, 𝑦, 𝑣), 𝑣 < 0.5 → GPLimit(𝑥, 𝑦, 0.5 − 𝑣) (2)
Tx(𝑥, 𝑦, 𝑤), GPLimit(𝑥, 𝑦, ℎ), w