Review Comment:
Review: Submission 2447-3661
The paper proposes a computational approach to modelling and resolving certain normative conflicts in legal reasoning, in particular those arising from defeasible rules. In such cases, different rules are applicable in different situations, and the appropriate rule has to be selected to determine, for example, which penalty is applicable. A solution to this problem would also address the double jeopardy principle, which determines that an individual may only be penalised once for any given offence.
The reasoning support required needs to incorporate preferential exception handling in a systematic way, something that classical ontologies cannot provide. The paper makes a persuasive case that preferential description logics do provide suitable reasoning support to model and reason about these legal regulations. The topic is relevant to the scope of the journal and makes a useful contribution to the application of defeasible ontologies. However, the paper is not publishable in its current form, due to a large number of (often minor, but sometimes important) issues that should be addressed. These include some technical issues that need to be ironed out.
The authors sometimes use the terms “exceptional” and “typical” in the technical sense in which these terms are defined in defeasible DLs, when their use is however linguistically counter-intuitive. For example, on p2-c2-line 8 (page 2, column 2, line 8), robbery is deemed more exceptional than theft. This creates the impression that theft (without any further knowledge of whether it was accompanied by violence) is more common than theft with further knowledge that it was accompanied by violence. What is presumably meant is simply that theft is a more general category, and robbery is a subcategory, and hence more exceptional. So robbery is a more specific crime category than theft, rather than more exceptional. Using the term “exceptional” here is misleading. There are a number of similar instances, also related to the use of “typical”. If most acts of stealing are characterised by violence, how can theft without violence be called typical, and robbery an exception? On p5-c1-line 20, defeasible subsumption is defined “to axiomatise exceptions for the typical objects”. This makes the notion of typicality synonymous with absence of conflicting specific information. For example, a typical theft is one without violence. There is no reason to assume this. Typicality is a technical term used to refer to “minimal object in the preference order in any model”, but using it like this in an applied setting is in my view problematic and misleading.
The DL language chosen is SHIQ, but on p3-c2-line 9 you have nominals in the concept language. If they are not needed anywhere they should be removed here. Disjunctions are needed, and in Section 4.1 a normal form is introduced (though not formally) where the antecedent of axioms are only conjunctions. These include defeasible axioms, and there need to be some explanation (either in the background or in Section 4.1) justifying why the concept language is still SHIQ. Can one always rewrite a defeasible axiom in this form, or does this impose some restriction on the concept language, or on what can be defeasibly stated?
In Definition 2.2, a model of a concept C is defined as any interpretation in which C has a non-empty extension. “In addition, …” There are two problems with this definition: Firstly, the semantics of axioms (subsumption axioms and instance axioms) haven’t been defined yet, so one cannot define the notion of a model of a TBox or ABox yet. Secondly, all concepts are interpreted in all interpretations, sometimes as the empty set. It doesn’t make sense to link the notion of a model of a knowledge base to some concept having a nonempty interpretation. The definition should move down to after line 29, and the two notions should be separated.
The discussion on p6 after Definition 2.5 doesn’t capture the point of why preferential reasoning is too weak. The fact that monotonicity fails doesn’t in itself show that preferential reasoning is too weak. The issue is the absence of the additional precondition of (RM) which is ignored in preferential entailment.
Definition 2.6 misses the criterion that a minimal model should exist and must either be unique, or there must be some predefined way to select one of the minimal models. Then on p6-c2-line 10, it would be useful to relate the presumption of typicality to the notion of a minimal model. On p6-c2-line 20, Is Figure 1 any possible interpretation, or how does it relate to the minimal model?
The focus of the paper is on one specific type of conflict, but presumably the penal code contains all three kinds discussed in Section 3.1. So the usefulness of the defeasible DL formalism would be very limited if the other types cannot be handled. Can they already be modelled in classical DL? That would be both important and useful to point out and briefly discuss.
There is something wrong with the classical example in Figure 3. At present, the classical ontology does not entail that Robbery is subsumed by Theft. Here is a similar example: Every girl is female. Every girl with blue eyes is a person. But it doesn’t follow that every person is female. The penalties also don’t follow. Perhaps a missing disjointness statement between RobberyPenalty and TheftPenalty?
It would be useful to refer to rationality (RM) on p12-c2 a bit earlier than is done at present, in the inference on line 16. In the discussion on lines 30-34, there is something more that needs to be explained. The RM property ensures that the typicality of all objects are maximised. The axiom on line 37 targets a specific set of objects — namely those in the extension of Event \sqcap \exists realizedThrough.Steal. But the axiom isn’t what effects the maximisation of typicality — instead, it constrains them to also belong to the RHS concept. So the preceding explanation doesn’t really explain the addition of the axiom.
Is it reasonable to impose the modelling restriction that the consequents in the ovverrule relation be disjoint? This seems to be required for the lemmas to follow, but was that the real reason for introducing the restriction, or does it also make intuitive sense? Some explanation of whether this is just a technical ploy or whether there is some other motivation is required. The lemmas themselves require a few important tweaks:
Lemma 1: The assumption should be that < is not irreflexive.
Lemma 2: Up to line 13 is fine, from which line 19 follows by the (AND) rule. So A(\alpha) is defeasibly subsumed by \bot. And that, I think, is all one can say. Indeed, if the antecedent is inconsistent, then asymmetry fails.
Lemma 3: The term intransitive usually means never transitive for any objects. You mean “not transitive”.
In Example 4.1, it is stated that it doesn’t make sense to claim the existence of two crimes, Robbery and Murder (p15-c1-line 50). It seems reasonable to have Robbery (without Murder) and also to have Murder (without Robbery). Is the point not rather that these are not required in the example?
Section 5 covers related work. It is quite extensive, and some of it is not directly linked to the application considered in the present paper. It could be trimmed but some might disagree.
Editorial comments:
Referencing: Don’t mix referencing styles, as in e.g. “Horrocks (2005)[17] …”. Either write “Horrocks (2005) …”, or just “Horrocks [17] …” This should be fixed throughout the paper.
p1-line 27: what it should -> t should
line 32: suits better -> is better suited
p1-c2-line 46: use -> used
line 48: reference or explanation required — why should a wider audience be served?
p2-c1-line 3: This is out by a decade — should be the start of the present century
line 7: allows to axiomatize -> allows the axiomatization / allows axiomatizing of
p2-c2-line 31: preferential DL is not a superset of classical DL — it is an extension of classical DL
p3-c1-lines 29-31: DLs are well-behaved fragments of .. Clarify that not all DLs are equally expressive — some are quite inexpressive, and others very expressive.
p4-c1-line 1: Avoid unnecessary capitalisation (e.g. “An Interpretation” should be “An interpretation”). Also throughout the paper, as with “Model” in line 8.
p5-c1-line 4: iot -> IoT (in the acronym the capitalisation is required)
p6-c1 lines 47-51: Remove “P \Vdash “
p6-c2-line 3: Remove “= T \cup A“ as this has already been established in the previous definiton.
p7-c1-lines 44-46: The issue is not really that it is computationally expensive, but rather that it is difficult, requires intensive maintenance and remodelling, etc.
p7-c46-line 46: Compliance -> compliance
p8-c1-line 49: e1 and e2 individuals -> individuals e1 and e2
p10-c1-line 5: on -> of.
line 19: Conversely, Perdurants … -> In contrast, perdurants … (“Conversely” means something more specific.) Ditto p10-c2-line 8.
p12-c2-line 2: The latter -> These
p14-c2-line 2: Only for -> For
p15-c1-line 43: whether -> when
p15-c2-line 51:call -> calls / a call?
p16-c1-line 2: DIP tab -> the DIP user interface (or something a bit more descriptive than “DIP tab”).
p16-c2-lines 25-36: Either remove “proposed by” and just keep the reference in each case, or insert the name of the author(s) in each case.
p17 Figure 8: This hand-drawn line and arrow are really ugly.
Throughout the paper: The font used in many of the displayed knowledge bases is very small, and without any good reason. E.g. on p18-c1-line 48, the font is quite readable, but then in c2-lines 13-14 it is tiny. Why not make the font the same size throughout?
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