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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Modular-PROLEG for Private International Law</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Takahiro Sawasaki</string-name>
          <email>tsawasaki@nii.ac.jp</email>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ken Satoh</string-name>
          <email>ksatoh@nii.ac.jp</email>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Aurore Clément Troussel</string-name>
          <email>aurore.troussel@umontreal.ca</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Cyberjustice Laboratory, Faculty of Law, Université de Montréal</institution>
          ,
          <addr-line>C.P. 6128, Downtown Branch</addr-line>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Montreal (Quebec)</institution>
          ,
          <country country="CA">Canada</country>
          ,
          <addr-line>H3C 3J7</addr-line>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>National Institute of Informatics</institution>
          ,
          <addr-line>2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430</addr-line>
          ,
          <country country="JP">Japan</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2022</year>
      </pub-date>
      <abstract>
        <p>When a legal dispute involves the laws of two or more countries, private international law resolves the conflict of laws by identifying which country has jurisdiction over the case and which national law applies. The automation of reasoning in the choices of jurisdiction and law has been done by Modular-PROLEG for PIL. The paper presents a new use case of Modular-PROLEG for PIL in which one must choose EU's General Data Protection Regulation (GDPR) or Japan's law on the data protection according to Japan's private international law. legal reasoning, private international law, choice of jurisdiction, choice of law, GDPR, PROLEG Joint Proceedings of ISWC2022 Workshops: the International Workshop on Artificial Intelligence Technologies for Legal Documents (AI4LEGAL) and the International Workshop on Knowledge Graph</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>When a legal dispute involves the laws of two or more countries, private international law
resolves the conflict of laws by identifying which country has jurisdiction over the case and
which national law applies. To automate the complex process which private international
law (PIL) performs, Satoh et al. [1] implemented a meta-interpreter Modular-PROLEG
for PIL which automatically reasons about the choice of jurisdiction and law in the
context of a dispute over legitimate parent-child relationship.</p>
      <p>In this paper, we use Modular-PROLEG for PIL in a new context : a transfer of personal
data between three countries. The question is which law between the EU’s General Data
Protection Regulation (GDPR) and the Japanese data protection law should apply to
the transfer according to Japan’s PIL. This case illustrates how Modular-PROLEG for
PIL can be used in practice.</p>
      <p>Related works include the one of Dung and Sartor [2] which provide an analysis of
private international law and propose a formal model based on a framework called
modular argumentation, which is an instance of abstract argumentation defined as a
pair (, )
of a set 
of arguments and a binary relation 
on 
[3]. Also,
(A. C. Troussel)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution
4.0 International (CC BY 4.0).</p>
      <p>CEUR
Workshop
Proceedings
htp:/ceur-ws.org CEUR
ISN1613-073</p>
      <p>Workshop Proceedings (CEUR-WS.org)</p>
      <sec id="sec-1-1">
        <title>2.1. Syntax</title>
        <p>•  # ⇐ 
•  ( #, ) ⇐ 
• ( #, #)
Calegari et al. [4] implement a reasoning about jurisdiction using a framework called
Arg-tuProlog, which is a lightweight modular argumentation inspired by [2]. Markovich [5]
uses the input/output logic introduced in [6] to specify rules in PIL. The advantage of
Modular-PROLEG for PIL over these works is that it identify both jurisdiction and law in
international legal dispute. Another related work is Governatori et al. [7], which presents
a comprehensive computational framework on the PIL’s reasoning patterns modeled by
[2, 8, 9]. In addition to reason about the choice of law and jurisdiction, this framework
allows to reflect about interpretive arguments. However, unlike Modular-PROLEG for
PIL, this framework is not a specific implementation of the reasoning about the choice of
jurisdiction and law. Modular-PROLEG for PIL also difers from PROLEG developed in
[10] mainly in that PROLEG cannot reason about the choice of law.</p>
        <p>The paper proceeds as follows. Section 2 briefly introduces Modular-PROLEG for PIL
implemented in [1]. Section 3 presents a hypothetical case in which several laws including
GDPR are involved and identifies the applicable laws in order to accept or reject the
claims made in the case. Section 4 illustrates how we implemented the reasoning found in
Case of Data Transfer by Modular-PROLEG for PIL, confirming that our implementation
returns the answers corresponding to the acceptance or rejection of the claims made in
Section 3.</p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. Modular-PROLEG for PIL</title>
      <p>In this section, we refer to [1] to briefly introduce the syntax and meta-interpreter of
Modular-PROLEG for PIL.1 We skip the semantics here since it is less relevant to seeing
a use case of Modular-PROLEG for PIL. See [1, p. 8] for the details.</p>
      <p>We refer to a Horn clause in either of the following forms as a rule:
1# 1, ⋯ ,   #</p>
      <p>1# 1, ⋯ ,   # 
where  ,   are atomic formulas and ,   ,  are variables. We call  # and  ( #, )
as the head of each rule, and   #  s as requisites of each rule. When  =   for all  ⩽  , we
often write the above rules as ( ⇐  1, ⋯ ,   )# and ( ( , ) ⇐  1, ⋯ ,   )# . The
intended readings of  # and  ( , )# are “  holds under the law of country  ”
and “the law of country  applies the law of country  to  ,” respectively. We also refer
to expressions of the following forms as exception and fact:</p>
      <p>1There are two diferences on Modular-PROLEG for PIL. First, in [ 1] the set ℛ may contain exceptions,
but may not in our paper. This change is only for readability. Second, where a country has no explicit
specification of choice of law regarding a case, the meta-interpreter in our paper chooses the law of the
country as the applicable law.
where ( #, #) is often written as ( , )# . We read them as “  is an
exception of  under the law of country  ” and “  is a fact under the law of country  ,”
respectively.</p>
      <p>A program  of Modular-PROLEG for PIL is a tuple (ℛ, ℰ , ℱ ) of finite sets ℛ, ℰ, ℱ
consisting of rules, exceptions and facts, respectively.</p>
      <sec id="sec-2-1">
        <title>2.2. Meta-Interpreter of Modular-PROLEG for PIL</title>
        <p>Here is the meta-interpreter of Modular-PROLEG for PIL (Algorithm 1, 2).2
Algorithm 1 Modular-PROLEG Meta-Interpreter for PIL</p>
        <p>pilprove() goal set 
1: if  == ∅ then return(∅);
2: for all atom # ∈  do
3: if # is an atom s.t.  ( #) ∈ ℱ
4:  ≔ ( − { # });
5: return(pilprove())
6: else % # should be a head in some rules
7:  ≔ choice_of_law(#, {}) ;
8: select a rule ( ⇐  1, … ,   )# ∈ ℛ</p>
        <p>by mgu ;
9: if such a rule does not exist then return(false);
10:  ≔ (( − { # }) ∪ {  1#, … ,   # }) ;
11: if pilprove() ==  by mgu  then
12: for all (, )# ∈ ℰ s.t. (#)
13: if pilprove({ (#) }) then return(false);
14: return()
15: else if pilprove() == false then return(false)
and  # is unifiable with #</p>
        <p>by mgu  then
where its head  #</p>
        <p>is unifiable with #
is unifiable with #
by mgu  do
Algorithm 2 Choice of Law</p>
        <p>choice_of_law(#,       ) #: a goal
1: if  ∈       then return()
2: else if  ==  (_, _) then return()
3: else if  (, {  (, )# }) ==  (#, ) by mgu  then
4: return(choice_of_law((#), {  } ∪       ))
5: else return() % choose a law of home country if there are no specifications of
choice of law
2Unfortuately, the current version of Modulr-PROLEG for PIL cannot generate the graphical schema
of the legal reasoning from a given program. To see how these algorithms work, see [1].</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. A Case on Transfer of Personal Data among Three Countries</title>
      <p>A use case on legitimate parent-child relationship in Japan has already been presented in
[1, p. 2–3]. In this section, we present a new use case of Modular-PROLEG for PIL in
which one must invoke the laws of two or more countries including GDPR.</p>
      <p>Let us consider the following hypothetical case on transfers of personal data between
three countries, hereinafter “Case of Data Transfer”:</p>
      <p>Case of Data Transfer A Japanese company who is established in Japan has
two branch ofices. One is in Country 1 inside the EU and the other is in
Country 2 outside the EU. To compare and monitor the productivity of its
employees in its diferent ofices, the company constantly performs transfers
of data of the employees between Japan, Country 1 and Country 2. The
employees and the company agreed on a contract (1) according to which
the employees might work in collaboration with Country 1’s ofice for specific
tasks. In addition, the employees and the company signed another contract
(12) according to which the employees who collaborated with Country 1’s
ofice might work with Country 2’s ofice. The two contracts briefly mention
that employees’ data such as name and job position might be transferred to
other ofices in order to allow personnel transfer. None of these contracts
explained to the employees that their data will be transferred to Country
1 and Country 2’s ofices to compare and monitor their productivity with
other employees. The company has not obtained any explicit agreement on
these data transfers from the employees. Furthermore, the company has not
provided any appropriate safeguard on the data transfers and Country 2 does
not benefit from an adequate level of data protection according to EU law
(i.e., Country 2 does not have an adequacy decision). Some of the employees
working at the main ofice in Japan have questioned the situation, and finally
sued the company for damages because the company transferred their data
in breach of the contracts (1) and (12) . The employees and the company
agreed that the law that governs the formulation and efect of the contract
(1) is the Japanese law, and that the law of Country 1 governs those of the
contract (12).</p>
      <p>In recent years, cases involving international data transfers, such as Schrems II3, received
much attention, thus it is interesting to implement Modular-PROLEG for PIL in Case of
Data Transfer.</p>
      <p>The question is whether the employees’ claims for damages would be accepted. More
precisely, we wonder if the following litigations can succeed:
(1) The litigation of the employees of the Japan’s ofice against the Japanese company
for damages because the company transferred their data from Japan’s ofice to
Country 1’s ofice in breach of the contract (1);
3https://eur-lex.europa.eu/legal-content/en/TXT/?uri=CELEX:62018CJ0311
(12) The litigation of the employees of the Japan’s ofice against the Japanese company
for damages because the company transferred their data from Country 1’s ofice to
Country 2’s ofice in breach of the contract (12).</p>
      <p>In what follows, we assume that Japan has jurisdiction over the employees’ litigations and
that each of (1) and (12) ’s claims for damages are accepted if and only if the contested
data transfer is illegal under the applicable law.</p>
      <p>The following legal reasoning shows that (1) ’s claims for damages would not be
accepted: Japan has jurisdiction over the litigations involving the employees of Japan’s
ofice. Thus, the PIL of Japan, i.e., Act on General Rules for Application of Laws
(AGRAL),4 determines which country’s law governs the acceptance of (1) ’s claims.
Because (1) is grounded on the fact that the company breached the contract (1) , the
governing law of the acceptance of (1) ’s claims is the law that governs the formulation
and efect of the contract (1) . To identify the law that governs the contract (1) , we
refer to Article 7 of AGRAL:</p>
      <p>Article 7, AGRAL The formation and efect of a juridical act are governed
by the law of the place chosen by the parties at the time of the act.</p>
      <p>Under Japanese law, the contract (1) is a juridical act. In addition, in Case of Data
transfer, the employees and the company choose the Japanese law to govern the formation
and efect of the contract (1) . Thus, according to Article 7 of AGRAL, the Japanese
law is the applicable law that determines whether (1)’s claims are accepted.</p>
      <p>Now that the applicable law is identified, we can test whether (1) ’s claims are accepted
under the Japanese law. The legal question is whether the transfer of the employees’
data from Japan’s ofice to Country 1’s ofice is lawful. To answer this question, the most
relevant article is Article 24 of the Japanese law called Act on the Protection of Personal
Information (APPI).5</p>
      <p>
        Article 24, APPI A personal information handling business operator, except
in those cases set forth in each item of the preceding Article, paragraph (
        <xref ref-type="bibr" rid="ref1">1</xref>
        ),
shall, in case of providing personal data to a third party [...] in a foreign
country [...], in advance obtain a principal’s consent to the efect that he or
she approves the provision to a third party in a foreign country. [...]
The exceptional clause “except in those cases set forth in each item of the preceding
Article” does not apply to Case of Data Transfer. At a first glance, as the company did
not obtain an explicit agreement on the disputed data transfers from the employees, the
data transfer from the Japan’s ofice to the Country 1’s ofice could be considered as
illegal. However, as the receiver of personal data is a branch ofice of the company, it has
the same legal personality, and thus it is not considered as a third party under APPI.6
4http://www.japaneselawtranslation.go.jp/law/detail/?printID=&amp;id=3783&amp;re=02&amp;vm=02 (Mar. 22, 2022)
5http://www.japaneselawtranslation.go.jp/law/detail/?printID=&amp;id=2781&amp;vm=02&amp;re=02 (Mar. 22, 2022)
6See p. 45 and p. 5 of the two guidelines of APPI which are found at https://www.ppc.go.jp/files/pdf/
210101_guidlines01.pdf and https://www.ppc.go.jp/files/pdf/210101_guidlines02.pdf (Mar. 22, 2022), respectively
(Japanese only).
Therefore, it is not illegal to transfer the employees’ data from the Japan’s ofice to the
Country 1’s ofice without the employees’ agreement, from which it follows that (1) ’s
claims are not accepted.
      </p>
      <p>Conversely, the following legal reasoning shows that (12) ’s claims would be accepted:
Using the same legal argument as in (1) , we consider that the law that governs the
formation and efect of the contract (12) is the applicable law. The employees and the
company have chosen Country 1’s law to govern the contract (c12), thus it is Country
1’s law that determines the acceptance of (12) ’s claims. As Country’s 1 is in the EU, the
GDPR applies to the case.</p>
      <p>
        To know whether (12)’s claims are accepted, we need to know whether it is illegal to
transfer the employees’ data from Country 1’s ofice to Country 2’s ofice. The important
articles are Article 44 and Article 49(
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) of GDPR.7
      </p>
      <p>Article 44, GDPR Any transfer of personal data which are undergoing
processing or are intended for processing after transfer to a third country or to
an international organisation shall take place only if, subject to the other
provisions of this Regulation, the conditions laid down in this Chapter are
complied with by the controller [...].</p>
      <p>
        In a nutshell, Article 44 rules that any transfer of personal data to a third country is
prohibited by default. However, there are exceptional rules allowing such a transfer
(Articles 45, 46, 49(
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) etc.). Regarding Case of Data Transfer, Article 49(
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) is particularly
important.
      </p>
      <p>
        Article 49(
        <xref ref-type="bibr" rid="ref1">1</xref>
        ), GDPR In the absence of an adequacy decision [...] or of
appropriate safeguards [...], a transfer or a set of transfers of personal data to
a third country or an international organization shall take place only on one
of the following conditions:
(a) The data subject has explicitly consented to the proposed transfer, after
having been informed of the possible risks of such transfers for the data
subject due to the absence of an adequacy decision and appropriate
safeguards.
(b) The transfer is necessary for the performance of a contract between the
data subject and the controller or the implementation of pre-contractual
measures taken at the data subject’s request.
      </p>
      <p>Case of Data Transfer does not satisfy the conditions for the applications of exceptional
rules: Country 2 does not benefit from an adequacy decision with the EU, and the
company did not put in place appropriate safeguards to transfer data. In addition,
the employees did not explicitly consent to the transfer of data from Country 1 to
Country 2 and the transfers of data are not strictly necessary for the performance of the
contract (c12) as the goal of the transfers is to compare and monitor the productivity of
7https://gdpr-text.com/read/article-44/#para_gdpr-a-44 (Mar. 22, 2022)
⋮
employees. Therefore, it is illegal to transfer the employees’ data from Country 1’s ofice
to Country 2’s ofice, from which it follows that (12)’ claims are accepted.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Implementation of Reasoning in the Case</title>
      <p>In the previous section, we considered a hypothetical case named as Case of Data Transfer
in which (12) ’s claims are accepted but (1) ’s claims are not. In this section, we illustrate
how we implemented the reasoning found in Case of Data Transfer by Modular-PROLEG
for PIL.</p>
      <p>We used Modular-PROLEG for PIL to implement national laws with non-envoi rules,
private international laws with envoi rules, and exceptional laws with exceptions, together
with appropriate paraphrases if necessary.</p>
      <p>It is important to explain how negation-as-failure (NAF) is handled in
ModularPROLEG for PIL. Modular-PROLEG for PIL does not have a built-in predicate like
not/1 which functions as NAF, but legal texts usually have many negative expressions
like “in the absence of an adequacy decision”. Thus, we need a method to formalize these
expressions literally. Our method consist in adding the following three lines into every
program:
1: (negation(P) &lt;= call(true))#C.
2: exception(negation(P),P)#C.</p>
      <p>3: (envoi(negation(P),RC) &lt;= envoi(P,RC))#C.
where (i)  must be a ground term in testing ( ) s and (ii) the line 2 must be the
only exception of ( ) in the program. Technically  could be any ground term, but
practically it is supposed to be an atomic formula. The condition (i) is necessary because
programs without (i) can easily go into a loop. For example, a program consisting only
of a rule ( ⇐ ( _))#_ and the lines 1–3 for negation/1 goes into a loop given an
input  . The condition (ii) is necessary to make negation/1 function as NAF.</p>
      <p>The set of the lines 1–3 guarantees that negation/1 functions as NAF. The line 1 says
that the negation of an atomic formula succeeds by default, which means that if the
negation of an atomic formula fails, then its (only) exception must succeed. The line
2 says that an atomic formula is the exception of its negation, which means that if an
atomic formula succeeds then its negation must fail. Accordingly, they jointly say that
an atomic formula succeeds if and only if its negation fails. The line 3 is needed to make
sure that the selected law for ( ) is the same as the selected law for .</p>
      <p>It should also be noted that the above method correctly captures the notion of the
burden of proof. Consider a trial in which a defendant tries to claim that  is the case
according to some article “if  is not the case then  is the case”. In jurisprudence, the
proof of the negation of something is very dificult to provide and is called probatio
diabolica. For this reason, the defendant does not bear the burden of proof of the
negation of  in the trial. Instead, the plaintif bears the burden of proof of  . When
we implement this article as  ⇐ () , the above method correctly captures the
fact that the plaintif bears the burden of proof of  because then () succeeds by
default unless  succeeds.</p>
      <p>
        Below, Article 7 of AGRAL, Article 24 of APPI and Articles 44, 49(
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) of GDPR are
implemented with Modular-PROLEG for PIL.
      </p>
      <p>Article 7 of AGRAL has the form of a rule in Modular-PROLEG for PIL and can be
implemented straightforwardly as follows:
1: (formulationAndEffect(Pla,Def,Contract,RC) &lt;=
plaintiff(Pla),
defendant(Def),
jurisAct(Contract,Pla,Def),
agral(ArticleNum,[Contract,RC]))#ja.</p>
      <p>2: (agral(7,[Contract,RC]) &lt;= choseAtThatTime(parties(Contract),RC))#ja.
The line 1 describes the prerequisites of Article 7 and the related articles, and the line 2
describes the substantial condition of Article 7.</p>
      <p>
        Article 24 of APPI does not have the form of a rule in Modular-PROLEG for PIL,
thus it must be paraphrased to implement. We paraphrase it as a rule that any transfer
of personal data to a third party in a third country of Japan will be illegal by default,
except when the data subject gave his consent and in the specific situations listed in
Article 23(
        <xref ref-type="bibr" rid="ref1">1</xref>
        ). We thus implemented it as follows:
1: (illegal(transfer(S,G,Data)) &lt;= appi(ArticleNum,transfer(S,G,Data)))#ja.
2: (appi(24,transfer(S,G,Data)) &lt;=
operator(X,transfer(S,G,Data),appi),
recipient(Y,transfer(S,G,Data),appi),
inThirdCountry(Y,ja),
thirdParty(Y,X,appi),
transfer(S,G,Data)).
3: exception(appi(24,transfer(S,G,Data)),ex_appi(24,transfer(S,G,Data)))#ja.
4: (ex_appi(24,transfer(S,G,Data)) &lt;=
subj(Subj,Data),
consent(Subj,transfer(S,G,Data)))#ja.
5: (ex_appi(24,transfer(S,G,Data)) &lt;=
      </p>
      <p>ex_appi(23,1,transfer(S,G,Data)))#ja.</p>
      <p>
        Similarly, Article 44 of GDPR can be paraphrased as a rule that any transfer of
personal data to a third country out of EU is illegal by default, except when exceptional
rules like Article 49(
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) apply. It is implemented as follows:
1: (illegal(transfer(S,G,Data)) &lt;= gdpr(ArticleNum,transfer(S,G,Data)))#c1.
2: (gdpr(44,transfer(S,G,Data)) &lt;=
      </p>
      <p>inThirdCountry(G,eu),transfer(S,G,Data))#c1.
3: (exception(gdpr(44,transfer(S,G,Data)),ex_gdpr(44,transfer(S,G,Data))))#c1.</p>
      <p>
        Finally, Article 49(
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) of GDPR has the form of a rule with negations in
ModularPROLEG for PIL and can be implemented straightforwardly as follows:
1: (ex_gdpr(44,transfer(S,G,Data)) &lt;= gdpr(49,ParagraphNum,transfer(S,G,Data)))#c1.
2: (gdpr(49,1,transfer(S,G,Data)) &lt;=
countryOf(C,G),
negation(adequateDecision(eu,C,gdpr(
        <xref ref-type="bibr" rid="ref3">45,3</xref>
        ))),
ctrlPrcsr(CtrlPrcsr,transfer(S,G,Data),gdpr),
negation(asg(CtrlPrcsr,transfer(S,G,Data))),
gdpr(49,1,ItemNum,transfer(S,G,Data)))#c1.
3: (gdpr(49,1,a,transfer(S,G,Data)) &lt;=
subj(Subj,Data),
consent(Subj,transfer(S,G,Data)),
knowRiskBeforeConsent(Subj,transfer(S,G,Data),
consent(Subj,transfer(S,G,Data))))#c1.
4: (gdpr(49,1,b,transfer(S,G,Data)) &lt;=
subj(Subj,Data),
ctrlr(CtrlPrcsr,transfer(S,G,Data),gdpr),
contract(Contract,Subj,CtrlPrcsr),
need(performance(Contract),transfer(S,G,Data)))#c1.
5: (gdpr(49,1,b,transfer(S,G,Data)) &lt;=
subj(Subj,Data),
ctrlr(CtrlPrcsr,transfer(S,G,Data),gdpr),
preContMeasure(Measure,Subj,CtrlPrcsr),
need(implement(Measure),transfer(S,G,Data)))#c1.
      </p>
      <p>⋯
where     ( ,    (, , ),  ) means that an agent is the controller or
processor of a transfer of data and (    ,    (, , )) means that the controller
or processor has provided appropriate safeguards for a transfer of data.</p>
      <p>
        The paragraphs above illustrated our implementation for Case of Data Transfer. In
Section 3, we wondered if the litigations (1) and (12) succeeded, i.e., (1) and (12) ’s
claims for damages were accepted. Below, we present how their claims are implemented
with Modular-PROLEG for PIL:
(
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) claim(empl(o(ja)),co,inBreachOf(transfer(o(ja),o(c1),data(empl(o(ja)))),cj1))#ja
(
        <xref ref-type="bibr" rid="ref2">2</xref>
        ) claim(empl(o(ja)),co,inBreachOf(transfer(o(c1),o(c2),data(empl(o(ja)))),c12))#ja
where ( ,  ,  ℎ (,  )) means that   ’s claims for damages
against  are accepted because  is done in breach of   . Let  1 be the
program for Case of Data Transfer containing the above codes.8 If we query (
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) and (
        <xref ref-type="bibr" rid="ref2">2</xref>
        )
together with  1, the interpreter of Modular-PROLEG for PIL returns that (
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) is false
but (
        <xref ref-type="bibr" rid="ref2">2</xref>
        ) is true, which corresponds to our conclusion in Section 3 that (1) ’s claims are
not accepted but (12)’s claims are accepted.
      </p>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion</title>
      <p>This paper presents a new use case of Modular-PROLEG for PIL in the context of
international data transfers. The task is to identify which law applies between the
European data protection law (GDPR) and the Japanese data protection law (APPI)
according to Japan’s private international law (AGRAL). As a future work, it would be
interesting to provide a more detailed implementation of GDPR, APPI and AGRAL by
Modular-PROLEG for PIL. For example, in this paper we implemented the conditions
that someone is a processor in GDPR and that someone is an operator in APPI as mere
8See https://github.com/tsawasaki/mprolegpil-usecase
facts. However, GDPR and APPI actually give us the definitional rules of processor and
operator so that these conditions follow from more primitive facts. The implementation
of these definitional rules would allow us to start from the more primitive facts to check
that both of these condition succeed, which would more precisely reflect the real process
done by jurists.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>We thank Yuto Mori for making valuable comments on private international law of
Japan. This work was supported by JSPS KAKENHI Grant Numbers, JP17H06103
and JP19H05470, JSPS Topic-Setting Program to Advance Cutting-Edge Humanities
JPJS00119217216 and JST, AIP Trilateral AI Research, Grant Number JPMJCR20G4.
[9] A. Malerba, A. Rotolo, G. Governatori, A Logic for the Interpretation of Private
International Law, in: S. Rahman, M. Armgardt, H. C. N. Kvernenes (Eds.), New
Developments in Legal Reasoning and Logic: From Ancient Law to Modern Legal
Systems, volume 23 of Logic, Argumentation and Reasoning, Springer International
Publishing, 2021, pp. 149–169. doi:10.1007/978-3-030-70084-3_7.
[10] K. Satoh, K. Asai, T. Kogawa, M. Kubota, M. Nakamura, Y. Nishigai, K. Shirakawa,
C. Takano, PROLEG: An Implementation of the Presupposed Ultimate Fact
Theory of Japanese Civil Code by PROLOG Technology, in: New Frontiers in
Artificial Intelligence, Springer Berlin Heidelberg, 2011, pp. 153–164. doi: 10.1007/
978-3-642-25655-4_14.</p>
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