Results

The modeling of the Gender enumeration in paper [GuFi2019], page 8 corresponds to our modeling of the .Gender attribute in Figure PC-Gender using a T2 propagation ([DaPi2002], page 8). We believe that our modeling methodology is in line with this and not only complements the authors' approach, but also extends it to streamline Multi-Level Modeling (MLM). To solve the request for variable embodiment with respect to the life phase of a species, similar to our modeling of ^.Gender as a PC in Figure PC-Boolean, an additional PC ^.LifePhase is introduced with subclasses ^.Child, ^.Teenager, ^.Adult, and ^.deceased where e.g., (^.deceased, »is, ^.LifePhase) and (^.deceased, .LifePhase, deceased). We can then model (>NPS-Carl-Linneaus, >^is, ^.deceased).

Compared to the modeling described in [CaAl2016], page 26, our approach allows the powertype MobilePhoneModel to be subsumed under its base type MobilePhone, while at the same time preserving the intended semantics. Using regularity attributes alone MobilePhoneModel cannot be subsumed under MobilePhone, because then each particular phone would then also have a launchDate. We successfully navigate around this modeling cliff by defining launchDate as a Universal Data Property (UDP) in the base type MobilePhone. Therefore, each particular would instantiate an imei or manufDate but not the launchDate. In addition, we are not required to add and maintain a property like potency [AtKu2001] to every data property. Our methodology dictates which instantiation rule is to apply by using the ^ symbol in UDP names (.^launchDate) or withholding it using Particular Data Property (PDP) names (.manufDate). As with deep instantiation, universals can have both instance and type character simultaneously. We believe that our modeling methodology not only complements the authors' approach, but also extends it to streamline Multi-Level Modeling (MLM).

With the results in the Evaluation section we have shown that the compromises mentioned in [WeLi2006] regarding the decision for expressiveness versus efficiency in reasoning can be significantly reduced by using partitioning classes. An essential prerequisite for this is again the use of the Value Assignment Propagation (VAP) method, without which PCs could not be used as described.

The conventional approach to modeling data properties is to define them directly in base classes such as ‘Person’, ‘Building’ and ‘Vehicle’, e.g. with (^Person, .Gender, :String). Alternatively, .Gender as shown in figure PC-Gender can also be modeled as partitioning class (PC) with (^.male, .∆Gender, male) and (^.female, .∆Gender, female). This method is suitable for any data property with an enumerable set of values. At the extreme, the orthogonal modeling method applied with the conventional modeling approach would be to model most of the data properties of a class as partitioning classes. The method is less suitable for data properties with continuous value dimensions such as ‘weight’, ‘length’, etc. Of course, this has implications for the inference and query methodology. It is therefore important to consider whether this is a step a modeler wants to take. And, of course, both modeling methods can also be used in parallel, which results in storage redundancy, but would then allow two different equivalent query methods in parallel. PCs can therefore be used to also explicitly assign all attribute values when inserting »pofs. This leads to more redundancy, but also has the potential to make queries much faster. Another advantage that we have worked out is that the number of particulars can be stored as meta information for each PC. This makes it possible, e.g., to determine how many ‘female’ and ‘male’ individuals are present without additional computation queries. As already addressed in the introduction section all examples in figure pc-gender, pc-colour, pc-boolean, and pc3, show that partitioning classes as introduced here take a place at the top of the inheritance hierarchies. We mark the methodological difference between partitioning classes and regular domain classes by using the relation »is instead of »subClassOf, e.g., (^Bird, »is, ^.warm-blooded).

Many other MLM approaches require properties such as potency, durability and mutability. E.g., in DeepJava the potency of an element denotes the maximum depth of its instantiation chain, or how many times a type can be instantiated. This places a heavy burden on the modelers since any change in an inheritance hierarchy may require the manual renumbering of potencies. We get around this problem by introducing simple naming conventions for the four required data property types combined with rules for their instantiation. We also provide criteria and guidelines for selecting the appropriate data property type.

In the approach presented here, Partitioning Classes (PC) are used to streamline conceptual modeling, avoid redundancies, and to increase performance. The Value Assignment Propagation (VAP) method is a prerequisite for this. Unlike other MLM methods, it is only necessary to specify whether data properties are particular, universal, meta, or transparent data properties. During instantiation, attribute-value pairs are automatically propagated by Transparent Data Properties (TDPs), but not by the other data property types. By using partitioning classes and the VAP method, we have shown how to avoid certain computational and modeling cliffs and how conceptual modeling can be more reconciled with natural language. With the VAP Axioms PCPAx and PCCAx we have argued how PCs can be used for reasoning and entailment. In the Methodology section we also showed that entailment is available for the combination of relationship types and partitioning classes. We believe that by adding multiplicity and mutability, and the VAP method PCs open up new possibilities for conceptual modeling. Depending on the modeler's needs, they can be used as an alternative or in addition to traditional modeling methods.

When using PCs in reasoning for the execution of conjunctive queries (CQA), we have already found in random samples that there is potential for an increase in performance by several orders of magnitude. In future investigations we want to evaluate how this behaves depending on the number of combined attributes and the size of the knowledge graph.