A rule-based deontic reasonerruleml.org/talks/XavierParent-RuleDeonticReasoner... · A rule-based deontic reasoner X. Parent RuleML Webinar 26th January 2018 University of Luxembourg

Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion

A rule-based deontic reasoner

X. Parent

RuleML Webinar 26th January 2018University of Luxembourg

Department of Computer Science

1Joint work with L. van der Torre

1 / 23A rule-based deontic reasoner

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Talk layout

1 Introduction

2 Benchmark problems

3 Our tool

4 How our solution works (roughly)

5 Conclusion


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Introduction

Background: AI & law

ReasoningMining

Legaltexts

1EU Horizon 2020 research and innovation programme–MarieSkodowska-Curie

Grant agreement No 690974.


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Introduction

Mining and reasoning

Norms(inmachine-

readableformat)

Alegaltext

2

Knowledgebase

(Automated)Deonticreasoner

data

ObligationsPermissionsLegal interpretationsEtc


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Introduction

Mining and reasoning

Norms(machine-

readableformat)

Alegaltext

2

Knowledgebase

Deonticreasoner

Long term-goal: automated tool supportNorm-compliance checkingConsistency checking


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Introduction

Example

5

6

Knowledgebase

DAPRECO

GDPRprovisos

ISOstandardséê

6

Knowledgebase

DAPRECO

GDPRprovisos

ISOstandardséê

L. Robaldo


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Introduction

Example

5

6

Knowledgebase

DAPRECO

GDPRprovisos

ISOstandardséê

6

Knowledgebase

DAPRECO

GDPRprovisos

ISOstandardséê

L. Robaldo


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Introduction

Deontic logic

Deontic logic

• Concerned with obligation, permission and related concepts• Normative reasoning in law• Sergot, McCarthy, Jones, Governatori, Sartor, ...• Law as a logical theory

Two research traditions

• Possible worlds semantics (mid 50s)• Deontic logic as a branch of modal logic

• “Norm-based”semantics (Hansen, 00s)• Roots in Alchourron and Bulygin’s ap-

proach to normative systems


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Introduction

Deontic logic

Deontic logic

• Concerned with obligation, permission and related concepts• Normative reasoning in law• Sergot, McCarthy, Jones, Governatori, Sartor, ...• Law as a logical theory

Two research traditions

• Possible worlds semantics (mid 50s)• Deontic logic as a branch of modal logic

• “Norm-based”semantics (Hansen, 00s)• Roots in Alchourron and Bulygin’s ap-

proach to normative systems

Rule-based systems


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Introduction

[Parent and van der Torre, 2017]

Parent, X. and van der Torre, L. W. N. (2017).The pragmatic oddity in a norm-based deontic logic.In Keppens, J. and Governatori, G., editors, Proc. of the 16th International Conference on ArticialIntelligence and Law, ICAIL 2017, London, United Kingdom, June 12-16, 2017, pages 169–178.

Highlights


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Introduction



Highlights

A “new” logic–in the rule-based tradition (I/O logic)

ý Well-definedý Performs well w.r.t. benchmark problems of deontic logic

• Contrary-to-duty (CTD) reasoning• Conflict

(Perform well=return the expected answers to queries)

Makinson/van der torre

RuleML 2015


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Introduction



Highlights

Advantage

ý Simple (on the outside)ý User-friendly

Easy to use for non-experts


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Introduction



Highlights

Novelty 1

ý Consistency checks in the semanticsý Reflected in the proof theory

Spin-off

ý Handles a recurrent objection against rule-based systems(e.g., Reiter’s default logic): lack of a proof-theory


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Introduction



Highlights

Novelty 2

ý A modular treatment of the two categories of benchmarks• A unique formalism, not two (separate) formalisms

Spin-off

ý The reasoner able to handle both CTDs and conflicts in thetext


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Benchmark problems

Group 1: CTD

The standard CTD structure (Chisholm)(1) a is obligatory(2) If not-a, then b is obligatory(3) If a, then not-b is obligatory

(4) Not-a

In the old days: SDLKD modal logicObligatory : true inthe ideal worlds

ProblemFormalisation

• Inconsistent

Overall: problem solved.But there are still prob-lems on the periphery.


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Benchmark problems

Group 1: CTD

The standard CTD structure (Chisholm)(1) a is obligatory(2) If not-a, then b is obligatory(3) If a, then not-b is obligatory

(4) Not-a



• Inconsistent


CTD obligation

ATD obligation

Primary obligation


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Benchmark problems

Group 1: CTD

The standard CTD structure (Chisholm)(1) a is obligatory(2) If not-a, then b is obligatory(3) If a, then not-b is obligatory(4) Not-a



• Inconsistent



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Benchmark problems

CTDs in the GDPR

Example 1

• Personal data shall be processed lawfully (Art. 5). Forexample, the data subject must have given consent to theprocessing of his or her personal data for one or more specificpurposes (Art. 6/1.a).• If the personal data have been processed unlawfully (none of

the requirements for a lawful processing applies), the con-troller has the obligation to erase the personal data in ques-tion without delay (Art. 17.d, right to be forgotten).


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Benchmark problems

Group 2: conflicts (cf. [Goble, 2013])

Normative conflict

The agent ought to do each of several things, but cannot dothem all

Goble, L. (2013).Prima facie norms, normative conflicts, and dilemmas.In Gabbay, D., Horty, J., Parent, X., van der Meyden, R., and van der Torre, L., editors, Handbookof Deontic Logic and Normative Systems, pages 241–352. College Publications, London. UK.


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Benchmark problems


Normative conflict


Strict, or simple, conflicts: ©a,©¬aBinary conflicts: ©a,©b but ¬♦(a ∧ b)N-ary conflicts (general form): ©a1, ...© an but ¬♦(a1 ∧ ... ∧ an)



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Benchmark problems


Normative conflict


Conflicts across regulations are common-place:

Must the user expressly provide consent to be tracked?ý GDPR: yesý New EU e-privacy directive : no.

The reasoner must be able to detect/accommodate inconsistencies.



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Benchmark problems


Normative conflict


State of the art with the modal logic approach: either the logic istoo strong or too weak:

ý Too strong: ©a,©¬a ` ©b (deontic explosion)ý Too weak: ©(a ∨ b),©¬a 6` ©b

Also missing: an integration with CTDs.



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Our tool

I/O logic (in a nutshell)

One of the success stories of deontic logic

• Devised by Makinson & van der Torre• Dedicated chapter in the Handbook of De-

ontic Logic

Conditionals (deontic reading): “If a, then b (obligation)”

• Semantics: “operational”• Procedures yielding outputs for inputs

• Proof-theory: generalizes existing ones• No axiom of identity (““If a, then a”” )• Principle not desirable under a deontic reading


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Our tool

A parenthesis on LegalRuleML

List of requirements (from the Oasis LegalRuleML TC)

Support for modelling:1 Different types of rules

• Prescriptive rules : obligations + permissions• Constitutive rules (counts-as conditionals)

Legal definitions (‘sensitive personal data’)Legal interpretation

2 Defeasible reasoning (reasoning about exceptions)

I/O logic ticks all the boxes!

Well-grounded in the legal domain


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Our tool

A parenthesis on LegalRuleML

List of requirements (from the Oasis LegalRuleML TC)

Support for modelling:1 Different types of rules

• Prescriptive rules : obligations + permissions• Constitutive rules (counts-as conditionals)

Legal definitions (‘sensitive personal data’)Legal interpretation

2 Defeasible reasoning (reasoning about exceptions)

I/O logic ticks all the boxes!

Well-grounded in the legal domain


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Our tool

Operational semanticsGeneral form

Below: a conditional obligation in the I/O notation

(a, x)| {z }also called a ‘rule’

14 / 17The pragmatic oddity in norm-based semantics

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a and x : two formulae of a base logic

A normative system N is a set of such pairs.

Advantage 2: simplicity and user-friendliness

Comes with the proof theory

a x

(a; x)

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What the reasoner does

Sample rules

(T)(a, x) (x , y)

(a, y)(OR)

(a, x) (b, x)

(a _ b, x)

8 / 21The pragmatic oddity in a norm-based semantics

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Main “semantical” construct:

x ∈ O(N, a)Given input a (state of affairs), x (obliga-

tion) is in the output under norms N

Detachment (modus-ponens) : core mechanism of the semantics


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Our tool





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a x

(a; x)

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Sample rules

(T)(a, x) (x , y)

(a, y)(OR)

(a, x) (b, x)

(a _ b, x)


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PL, FOL, modal logic, ...


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Our tool





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a x

(a; x)

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Sample rules

(T)(a, x) (x , y)

(a, y)(OR)

(a, x) (b, x)

(a _ b, x)


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??


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Our tool

Two-sided architecture

• Semantics!"#$%$&!!($%)"*+,&-&$&!!.&!#,-!

Proof-theoryDerivationtree

NodesarepairsofformulasInferencerules

I/Ooperations

Butneededfor,e.g.,decidabilityAndhiddentotheeyesofusers



a x

(a; x)

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Sample rules

(T)(a, x) (x , y)

(a, y)(OR)

(a, x) (b, x)

(a _ b, x)


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a x

(a; x)

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Underthehood Ontheoutside


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Our tool

A potential misunderstanding

“User-friendly” does not mean trivial.There is more to I/O logic than just deriving pairs frompairs.

When you see written(a, x)


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Our tool

A potential misunderstanding

“User-friendly” does not mean trivial.There is more to I/O logic than just deriving pairs frompairs.

When you see written(a, x)

Under the hood, the reasoner has calculated that



a x

(a; x)

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Sample rules

(T)(a, x) (x , y)

(a, y)(OR)

(a, x) (b, x)

(a _ b, x)


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x ∈ O(N, a)


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How our solution works (roughly)

Our proposal: a new I/O operationSemantics

Calculating the output: a 3-step procedure

Is there B ⊆ Cn(A) s.t.

Is x equivalent with

YesNo

B triggers finitely many obligations in N?

the conjunction of their heads ?

NoYes

x not in the output

x not in the output

Is B consistent with the hypothesis

(among those triggered) is fulfilled?

that an arbitrarily chosen obligation

Yes No

x not in the outputx in the output


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Our take on the benchmarks (roughly)Proof-theory

A modular treatment Weaken the logic, but not toomuch

The troublemakers:

(a, x) x ` yWO

(a, y)

(a, x) (a, y)AND

(a, x ∧ y)

It is okay to let WO go. It is not okay to let AND go.

A middle way

(a, x) (a, y) a ∧ x consistent a ∧ y consistentR-AND

(a, x ∧ y)


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The troublemakers:

(a, x) x ` yWO

(a, y)

(a, x) (a, y)AND

(a, x ∧ y)


Against AND: “pragmatic oddity” (Sergot/Prakken)

d : there is a dogs: there is warning sign

(>,¬d)SI

(d ,¬d) (d , s)AND

(d ,¬d ∧ s)

A middle way


(a, x ∧ y)

No!


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The troublemakers:

(a, x) x ` yWO

(a, y)

(a, x) (a, y)AND

(a, x ∧ y)


In support of AND (Horty)

Norms come from different sources ⇒ aggregation

m: military servicec: civilian

(>,m ∨ c) (>,¬m)

(>,¬m ∧ c)

A middle way


(a, x ∧ y)

Yes!


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The troublemakers:

(a, x) x ` yWO

(a, y)

(a, x) (a, y)AND

(a, x ∧ y)


A middle way


(a, x ∧ y)

Consistency checks


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EvaluationICAIL ’17, June 12-16, 2017, London, United Kingdom X. Parent and L. van der Torre

In this paper we only consider the simple minded I/O operationfrom Makinson and van der Torre [25]. The operation is writtenas O. Compared to their I/O operation, de�nition 4.4 has threesalient features. First, de�nition 4.4 requires x to be equivalent tothe conjunction of heads of rules in some M ✓ N , rather than tobe implied by such a conjunction. This has the e�ect of letting therule of weakening of the output go (see example 3.3 below). Second,de�nition 4.4 looks at what is triggered by some B ✓ Cn(A), insteadof looking at what is triggered by A. Third, de�nition 4.4 uses theconsistency proviso ii). The last two features give a “backward-looking" �avour to our account. To determine if x is obligatory, we(so to speak) go back in time, before the violation has occurred, andwe check if x was already obligatory at that point in time, in thesense of being equivalent with the conjunction of heads of rules insome M ✓ N .

De�nition 3.2. x 2 O(N ,A) i� there is a �nite set of norms M ✓N and a set B ✓ Cn(A) such that M(B) , ; and

i) x a` ^M(B)ii) For all (a,x) 2 M , we have {a,x} [ B is consistent

Curly brackets will be omitted for singleton input set A..In order to give the reader a taste of how the account works, we

apply it to a number of examples.Example 3.3 (Ross’ paradox). Let N = {(>,p), where p is for

posting a letter, A = {>}. p is outputted in context >, viz p 2O(N ,>). But p_b is not outputted in context >, viz p_b < O(N ,>).Intuitively, from the obligation to post a letter, one does not derivethe obligation to post a letter or burn it.

Example 3.4 (Pragmatic oddity). Let N = {(>,k), (¬k,a)} andA = {¬k}. k is outputted in context ¬k , viz k 2 O(N ,¬k). Intu-itively, once violated, the primary obligation to keep one’s promisestill holds. Hence the drowning possible is avoided. a is also out-putted in context ¬k , viz a 2 O(N ,¬k). Intuitively, the secondaryobligation to apologise is detached. But the joined obligation tokeep one’s promise and apologise for not keeping it does not hold,viz. k ^ a < O(N ,¬k).

Example 3.5 (Horty). Let N = {(>, f _ s), (>,¬f )} and A = {>}.s ^ ¬f is outputted in context >, viz s ^ ¬f 2 O(N ,>). Intuitively,the joined obligation to perform an alternative military service andnot go into the army is detached, as it should be.

In Table 1, we apply the account to some other well-knownexamples from literature. This will help the reader appreciate whatis going on. The �rst column contains a reference to the paperin which the example was �rst described. The second and thirdcolumn show a formalisation of the example in I/O logic, althoughmany of them were �rst introduced in monadic deontic logic. Thelast two columns show the output. A “yes" indicates a formula thatis outputted. A “no" indicates a formula that is not outputted.

Theorem 3.6 states that O is monotonic with respect to the inputset.

T�� 3.6 (M�� .�.�. ��). Given a set A of formu-lae and a formula a, we have O(N ,a) ✓ O(N ,A) whenever a 2 Cn(A).

P��. Assume x 2 O(N ,a) and a 2 Cn(A). From the �rstassumption, there is some �nite M ✓ N and some B ✓ Cn(a) suchthat M(B) , ; and

Table 1: Deontic benchmark examples

N A yes no[5] (>, ¬k ), (k, k ^ �) k ¬k , k ^ � ?[30] (>, ¬c), (k, c) k ¬c , c , ?[18] (>, ¬f 0), (a, f 0) a ¬f 0, f 0, ?[30] (>, ¬f ), (f , f ^ w ), (d, f ) d ¬f , f , ?[37] (r, c0) r ^ s c0

(r, c0), (s, ¬c0) r ^ s c0, ¬c0 ?[35] (>, p), (>, ¬p) > p, ¬p, ?[36] (>, p) ¬(p ^ h) p

(>, p), (>, h) ¬(p ^ h) p, h, p ^ h p ^ ¬h[31] (>, ¬d ), (d, d ^ p0) d ¬d , d ^ p0, ?

(>, ¬(d ^ p0) ¬(d ^ p0)k : kill c : cigarette p : polite�: gently d : dog h: honestf : fence r : rain a: asparagusw : white s : sun c 0: closef 0: �nger p0: poodle

i) x a` ^M(B)ii) For all (a,x) 2 M , we have {a,x} [ B is consistent

From the second assumption, {a} ✓ Cn(A), and so Cn(a) ✓ Cn(A),by monotony for ` and idempotence. Hence B ✓ Cn(A), whichsu�ces for x 2 O(N ,A). ⇤

3.3 Proof theoryDe�nition 3.7 (Proof system). (a,x) 2 D?(N ) if and only if (a,x)

is derivable from N using the rules {SI, EQ, R-AGGR}.

(a,x) b ` aSI (b,x)

(a,x) x a` �EQ (a,�)

(a,x) (a,�)R-AGGR a ^ x and a ^ � are consistent(a,x ^ �)

Furthermore, for each leave (b,�) in the derivation, b^� is requiredto be consistent.

SI stands for “strengthening of the input". EQ stands for “equiva-lence". R-AGGR stands for “restricted aggregation".

Where A is a set of formulae, (A,x) 2 D?(N ) means that (a,x) 2D?(N ), for some conjunctiona of elements inA. Moreover,D?(N ,A)is {x : (A,x) 2 D?(N )}.

P�� 3.8. Given SI, R-AGGR is equivalent to

(a,x) (b,�)R-AGGR0 a ^ b ^ x and a ^ b ^ � are consistent(a ^ b,x ^ �)

P��.• R-AGGR ) R-AGGR0. The last step in the derivation below

goes through, because a ^b ^ x and a ^b ^� are assumedto be consistent.

(a,x)SI (a ^ b,x)

(b,�)SI (a ^ b,�)

R-AGGR (a ^ b,x ^ �)

Good news : reasoner returns the expected answers.


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Conclusion

Summary

I have described a deontic reasoner currently under development.ý Well-defined:

Semantics and proof-theory

Completeness result linking the two

ý Performs well on the two categories of benchmark problems ofdeontic logic

Spin-off: allows us to address a recurrent objection againstrule-based systemsý Lack of proof-theory


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Conclusion

Future work

A big step forward, but only a first step.

Extensions

ý Time, exceptions and other natural language constructsý Permission and constitutive rules

Automation

ý On-going work, with Benzmuller• Embedding into Higher-Order Logic (HOL)• Theorem-prover Isabelle/HOL for automation


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Thank you!


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Conclusion

Non-monotonic logics & CTDs

Flavored by, e.g., McCarthy (early 90’s)

Bottom line

(>,¬d)SI

(d ,¬d)Dashed line: the inference isblocked.

Sergot’s view: no good for norm-compliance checking


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xav


Conclusion

Non-monotonic logics & CTDs

Flavored by, e.g., McCarthy (early 90’s)

Bottom line

(>,¬d)SI

(d ,¬d)Dashed line: the inference isblocked.

“The non-monotonic properties of a logic program usingnegation-by-failure make a consistent representation [of CTDs]possible. However, the program will have certain counter-intuitiveproperties. For instance, violated obligations simply vanish. Nothingmore can be inferred about them, as the condition for somethingbeing obligatory no longer applies. One might argue that in actuallife violated obligations do not vanish.” (Herrestad)


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Documents

A rule-based deontic reasonerruleml.org/talks/XavierParent-RuleDeonticReasoner... · A rule-based deontic reasoner X. Parent RuleML Webinar 26th January 2018 University of Luxembourg