LyX Document

Encoding values

There are certain functions expecting data values to be passed to them. To be able to do that in a uniform way, RAAPI expects data values to be passed as strings. The following table explains how values of different data types are converted to strings:

Type	How encoded
String	as is (we assume that UNICODE characters ‘INFORMATION SEPARATOR ONE’, ‘INFORMATION SEPARATOR TWO’, ‘INFORMATION SEPARATOR THREE’, ‘INFORMATION SEPARATOR FOUR’, ‘CANCEL’, ‘END OF TEXT’, and ‘NULL’ are not used in String values)
Integer	converted to a string using the decimal notation (with a “-” sign in the beginning for negative integers)
Real	converted to a string using the decimal notation and a dot (“.”) as a decimal point
Boolean	either the string value “true”, or “false” (all letters are small)
void or null (to indicate no value)	a string consisting of a single Unicode character U+0018 (CANCEL); this value is essential to distinguish between null values and empty strings, when calling methods
a collection of some type from above	each collection element is encoded according to the rules above; elements are delimited by the UNICODE character U+001F (INFORMATION SEPARATOR ONE)

LyX Document

On Meta-Levels

You may wish to read more on models at http://webappos.org/theory/models.

Linguistic vs. Ontological Metamodelling

Atkinson and Kühne [2, 6, 5] noticed that actually there are two variants of the ``instance of'' relation: ``linguistic instance of'' and ``ontological instance of''. Thus, meta-levels can also be linguistic and ontological. To see the difference between these two types of meta-levels, refer to Figure #. Figure #(a) is an example of UML Four-level Metamodel Hierarchy [#bib_uml_infrastructure]. Although Level M0 (a level of real world objects) lies outside MOF TS, it is depicted for informative purposes. ECore is a possible meta-metamodel for Level M3 (only a small part of it is depicted in Figure #(a)). Level M2 contains a UML-like metamodel described in ECore. For this example it is essential that the M2 Level metamodel is able to describe both classes and objects, see classes Class and Object. Level M1 contains a sample model, which conforms to the UML-like metamodel from Level M2.

All the three levels (M1-M3) are linguistic meta-levels, since the meta-metamodel from Level M3 can be considered a language for specifying metamodels at Level M2, and each metamodel from M2 can be considered a language for specifying models at M1. However, if we look at Level M1 more narrowly, we can see that it can be split into two levels, where UML-style objects occupy one level, and UML-style classes occupy another level (Figure #(b)). The borderline is defined by the ``type'' relation from Level M2. These new levels are called ontological meta-levels. They are denoted

O_{j}

and

O_{j + 1}

in Figure #(b), while linguistic meta-levels (M1-M3) have been renamed to

L_{i}, L_{i + 1},

and

L_{i + 2} .

The pivot indices

i

and

j

have been introduced here to be independent on any particular absolute numbering

Different authors may use different absolute numbering. For instance, et al. use

L_{1}

and

L_{2}

for

L_{i}

and

L_{i + 1}

[3], while Atkinson and use

L_{0}

and

L_{1}

[2].

. For the purposes of this thesis, only relative arrangement of (both linguistic and ontological) meta-levels will matter.

Figure #(c) adds one more ontological meta-level

O_{j + 1}

by introducing the MetaClass concept at

L_{i + 1}

. However, in order to express the six-meta-level example by D. Hofstadter, we must add at least three more meta-classes at

L_{i + 1}

(in order the total number of ontological meta-levels become six). Figure #(d) shows that instead of introducing meta-class(es), multiple ontological levels can be described by means of the ``type'' relation from Class to Class at

L_{i + 1}

. This relation can be used as many times as needed, thus, creating a chain of ontological meta-levels as in the example by D. Hofstadter (the ``lowest'' meta-level can be linked to the chain by the ``type'' relation between Object and Class).

In Figure #(d), Class can also be made a subclass of Object at

L_{i + 1}

(Atkinson and [1] introduce the term ``clabjects'' [from class+object] for such classes). In this case, the ``type'' relation between Object and Class is not needed any more, since its role is played by the ``type'' relation from Class to Class.

In some cases ontological meta-levels can be mixed. In Figure #, a class Person has been added. A person can be linked to a dog by means of the ``owner'' relation defined at Level

O_{j + 1}

. A person can also be linked to a breed by means of the ``favourite breed'' relation, which crosses levels

O_{j + 1}

and

O_{j + 2}

. Having a particular person Peter at

O_{j}

, we can see that the ``owner'' link lies in the same

O_{j}

level, while the ``favourite breed'' link crosses two levels

O_{j}

and

O_{j + 1}

image: 4D___publications_thesis_figures_fig_meta_levels_mix.png

Figure 2: Mixing ontological meta-levels. The ``favourite breed'' relation between Person and Breed as well as the link between Peter and Collie cross two adjacent meta-levels.

The theory behind the ``instance of'' relation goes even further. , Kaviani, and Hatala show that the (ontological) ``instance of'' relation can be inferred from the two other relations. They suggest to treat each class as consisting of two parts: intentional and extensional [3]. Intentional part specifies common features of objects (e.g., ``has long hair'') and is used for building abstractions; the relation between elements and the intentional part is called ``conformant to''

This is not the same as ``conforms to'' defined above.

. Extensional part represents a class as a set, to which certain elements (objects) belong; the relation between elements and the extensional part is called ``element of''. For the purposes of this thesis I do not need the ``conformant to'' and ``element of'' relations. Still, I will need both variants (linguistic and ontological) of the ``instance of'' relation.

On the one hand, multiple ontological meta-levels and (usually) the three linguistic meta-levels give power to describe and organize models. On the other hand, it appears that it is difficult for a human to concentrate at more than two meta-levels at a time. While working on a generator for higher order model transformations

this term is explained below

, where multiple meta-levels are involved, A. Šostaks came to the following conclusion (I call it Šostaks' conjecture):

It is difficult for a human to think at more than two meta-levels at a time. Still, it is fairly easy for a human to focus on any two adjacent meta-levels
4
This conjecture has been mentioned by Agris Šostaks during a personal conversation. The conjecture has been published in one of my papers [4].

.

One of the arguments in favour of this conjecture is as follows. Students learning Java can work with classes and objects easily (two meta-levels are used). Java is an object-oriented language, and it has the Object class, which is a common superclass for all other classes — an easy-to-understand OOP construction. At the same time, Java has the reflection mechanism, which permits considering Java classes as objects. The class named Class has been introduced for that. Actually, it is a meta-class (i.e., it brings an additional meta-level to Java), but represented as an ordinary Java class. At this point students encounter difficulties, since three meta-levels are involved

Personal conversations with Edgars Celms.

Certain RDF/OWL meta-levels can be considered either linguistic, or ontological. In Table table:technical_spaces, RDF can be considered as spanning three linguistic meta-levels: the RDFS level (M3), the RDF vocabulary level (M2), and the RDF individuals level (M1). Still, RDFS permits breaking this level hierarchy, since classes may be individuals at the same time. RDFS also allows meta-levels to be mixed (as in Figure #). The same refers to OWL Full and OWL 2 with RDFS semantics. Thus, we can think of RDF/OWL TS as occupying only two linguistic meta-levels:

L_{2}

containing RDFS/OWL Full definition, and

L_{1}

containing the pool of ontological classes and instances (

L_{1}

conforms to

L_{2}

). In this case,

L_{1}

consists of two or more ontological meta-levels, which can be mixed. To deal with different interpretations of meta-levels (whether the given level is linguistic or ontological), I introduce quasi-meta-levels in Section # of this thesis.