Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion A rule-based deontic reasoner X. Parent RuleML Webinar 26th January 2018 University of Luxembourg Department of Computer Science 1 Joint work with L. van der Torre 1 / 23 A rule-based deontic reasoner N
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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
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
Talk layout
1 Introduction
2 Benchmark problems
3 Our tool
4 How our solution works (roughly)
5 Conclusion
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
Introduction
Background: AI & law
ReasoningMining
Legaltexts
1EU Horizon 2020 research and innovation programme–MarieSkodowska-Curie
Grant agreement No 690974.
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
Introduction
Mining and reasoning
Norms(inmachine-
readableformat)
Alegaltext
2
Knowledgebase
(Automated)Deonticreasoner
data
ObligationsPermissionsLegal interpretationsEtc
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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 Benchmark problems Our tool How our solution works (roughly) Conclusion
Introduction
Example
5
6
Knowledgebase
DAPRECO
GDPRprovisos
ISOstandardséê
6
Knowledgebase
DAPRECO
GDPRprovisos
ISOstandardséê
L. Robaldo
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
Introduction
Example
5
6
Knowledgebase
DAPRECO
GDPRprovisos
ISOstandardséê
6
Knowledgebase
DAPRECO
GDPRprovisos
ISOstandardséê
L. Robaldo
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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 Benchmark problems Our tool How our solution works (roughly) Conclusion
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 Benchmark problems Our tool How our solution works (roughly) Conclusion
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 Benchmark problems Our tool How our solution works (roughly) Conclusion
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
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 Benchmark problems Our tool How our solution works (roughly) Conclusion
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
Advantage
ý Simple (on the outside)ý User-friendly
Easy to use for non-experts
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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
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 Benchmark problems Our tool How our solution works (roughly) Conclusion
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
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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.
CTD obligation
ATD obligation
Primary obligation
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
Benchmark problems
Group 2: conflicts (cf. [Goble, 2013])
Normative conflict
The agent ought to do each of several things, but cannot dothem all
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.
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
Benchmark problems
Group 2: conflicts (cf. [Goble, 2013])
Normative conflict
The agent ought to do each of several things, but cannot dothem all
State of the art with the modal logic approach: either the logic istoo strong or too weak:
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
Our tool
A parenthesis on LegalRuleML
List of requirements (from the Oasis LegalRuleML TC)
8 / 21The pragmatic oddity in a norm-based semantics
N
a x
(a; x)
N
What the reasoner does
Underthehood Ontheoutside
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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
Advantage 2: simplicity and user-friendliness
Comes with the proof theory
a x
(a; x)
N
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
N
x ∈ O(N, a)
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
How our solution works (roughly)
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
How our solution works (roughly)
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.
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) (a, y) a ∧ x consistent a ∧ y consistentR-AND
(a, x ∧ y)
No!
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
How our solution works (roughly)
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.
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) (a, y) a ∧ x consistent a ∧ y consistentR-AND
(a, x ∧ y)
Yes!
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
How our solution works (roughly)
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)
Consistency checks
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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
How our solution works (roughly)
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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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Introduction Benchmark problems Our tool How our solution works (roughly) Conclusion
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)