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Summary

The article covers the issues of knowledge representation languages in domain ontologies: LOOM, OCML, OWL, FLogic, SHOE, RDF(S), Ontolingua, and OWL2. The aim of the undertaken and described studies is the evaluation of utility of these languages using the MLP method and the ability to improve the properties of the se-lected language, which has a high applicability in the construction of the domain on-tologies. The result is a ranking of languages based on the assessment in the form of MLP utility functions with preference attributes specified with the AHP method and also is to show the possibility of simulation and improvement of attribute properties of the selected language.

Keywords: knowledge representation, MLP, AHP, ontology, knowledge base Introduction

In the literature of computer science, the concept of ontology has appeared for the first time in 1967 in the work of S.H. Mealy in the context of data modelling [10]. It is assumed that ontology is an unambiguous specification of conceptualisation [9], which includes four meanings: (1) concep-tualisation, which is an abstract model exiled from the real world to represent certain concepts; (2) clarity, what means that no ontology has got the clearly defined concepts, relations, properties, func-tions, limitations and axioms; (3) formalisation, which means that the ontology can be understood and executed by a machine; (4) co-sharing, meaning that the ontology is a reflection of the generally recognised domain knowledge and it provides semantic services [15]. This definition refers to the fact that thanks to the ontology it is possible to present the domain knowledge, and then co-share this knowledge and use it multiple times. The problem arises on what methods should be used to assess the languages (their ranking and grouping), to select the one, which will be useful for the considered decision problem. It is important to take into account the preferences of the field expert. The article has also presented the rationale for the use of ontology as the knowledge representation formalism, the features of individual knowledge representation languages were indicated and their evaluations was conducted.

The aim of the studies undertaken and described in the article is the evaluation of the utility of the knowledge representation languages using the MLP method with the possibility of improving the properties of the selected language characterised by a high applicability in the construction of domain ontologies. The article has used the DSS 2.0 system, created by Becker J., Budziski R.2 Chapter 1 presents literature review about knowledge representation languages. Later, a MLP model

1 MLP – Multicriterion Linear Programming.

2 More about the DSS 2.0 in [2], which presents the organization of information structures for the needs of a complex,

multi-faceted (multi-methodical) decision analysis, the subject of which is a certain category of objects. The focus is on the discus-sion of the transformation of the information structure of partial mathematical models, reflecting the objects of analysis, to the form of records of the database and on their connection into a more complex structure, so-called multi-model, in order

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is defined and the application of DSS 2.0 system to solve the model is presented. Finally, the article summarizes the results.

1. Characteristics of the technology of knowledge representation languages

The selection and evaluation of the language for building the domain ontology is becoming a de-cision problem, which the expert of the given field faces. Since the individual languages are based on different formalisms and their combinations vary in the degree of formalisation, expressivity and complexity of inference. Dependencies between the formalisms underlying different ontology lan-guages are included in fig. 1.

Figure 1. Dependencies between formalisms underlying the ontology languages

Source: own study based on ([1], [6], [16]).

Generally, these languages can be divided into two groups: traditional languages and mark lan-guages. Traditional languages include, among others: Ontolingua, LOOM, OCML, FLogic. While the languages based on marks include, among others: SHOE, RDF(S), OWL and OWL_2.

The Ontolingua language is based on the I order logic, but it was additionally expanded with the frames. It allows the creation of elements, such as: concepts, concept taxonomies, n-ary relations, functions, axioms, instances and procedures. Due to the high expressivity, it is difficult to construct the interference mechanism for it [7], [5].

LOOM was developed as a language that allows the construction of expert systems, knowledge bases and other intelligent applications. It is embedded in the descriptive logic, and it consists of two sub-languages, i.e.: descriptive language, which counterpart in the descriptive logic comes in the form of TBox, and the link language, which counterpart in the descriptive logic comes in the form of ABox. LOOM is a monotone language. It enables the automatic classification of concepts, and contains the elements, like: concepts, concept taxonomies, n-ary relations, functions, axioms and production rules. Additionally, it supports the calculations of predicates and procedural pro-gramming. The disadvantage of the LOOM language is the fact that it is very expressive, and there-fore its inference mechanism does not allow the complete inference (LOOM is unsolvable) [7].

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OCML (Operational Conceptual Modelling Language) is based on the Ontolingua language (it uses the I order logic and frames), and it was built to develop the executable ontologies and problem-solving models. It allows you to define classes, relations, functions, axioms and instances, and to define the production and deduction rules and the procedural extensions. It contains 12 basic ontol-ogies containing: data types, definitions of primitives, which are the ontology elements (e.g. rela-tions), primitives used to construct problem solving methods and the description of the OCML lan-guage.

FLogic (Frame Logic) is based on the paradigm of object-oriented programming, framework and I order logic. Initially, the use of the FLogic language included the deductive and object databases, and only then it has been adapted for application in ontologies. FLogic enables the definition of concepts, concept taxonomies, binary relations, functions, instances, axioms and deductive rules. Inference mechanisms, intended for this language, are able to provide a full inference only for its monotone part [7], [5].

SHOE (Simple HTML Ontology Extension) was to introduce the semantic knowledge to Web documents. It was based on the framework and rules. Moreover, it can use the HTML or XML syntax. The SHOE language contains the representation of concepts, their taxonomy, n-ary relations, instances and deductive rules. The inference mechanism to acquire new knowledge uses the deduc-tive rules [7], [5].

RDF(S) (Resource Description Framework + Schema) is a combination of the RDF language based on semantic networks and RDFS language using the framework. Basically, the RDF(S) lan-guage (like its ancestors, i.e., RDF and RDFS) should not be strictly understood as the lanlan-guage of ontology, but rather as a general language of data description on the Internet. Therefore, this lan-guage is much less expressive than almost all previously characterised ones. It provides the repre-sentations of concepts, taxonomies and binary relations and uses the XML syntax. The operation of inference mechanisms for this language is mainly brought down to checking the constraints [7], [5]. OWL (Web Ontology Language) is designed for publishing and co-sharing ontologies on the Internet and it uses the XML and RDF syntax. OWL is a monotone language [7], [14]. There are three varieties of the OWL language in version 1 different in terms of expressivity. They are based on the descriptive logic, OWL Lite and OWL DL and, going beyond the descriptive logic, OWL Full. The varieties of OWL Lite and OWL DL are fully decidable and they allow full inferences, while OWL Full can be unsolvable, and the inference of this language can be very little predictable [8], [1], [11].

The OWL 2 language, compared to OWL in version 1, has allowed the creation of new structures, such as: keys, new data types, frequency limitations qualified through the data type, new properties (among others, the asymmetry and manoeuvrability, and separation of characteristics). Besides the full OWL 2 language (which is unsolvable), there are also language profiles: OWL 2 EL, OWL 2 QL and OWL 2 RL [8] [13]. Each of these profiles is based on a subset of descriptive logic, so also each of them is decidable and allows full inference. There is also an informal profile OWL 2 DL, limiting the OWL 2 language to the set of descriptive logic [4], [14].

To build the ontology representing knowledge in a certain field, one should select the appropriate language of its representation. This will allow the creation of knowledge base, where it will be pos-sible to conduct full, decidable inference. Formalisation of the utility of the discussed languages (construction of the knowledge base) requires the development of the precise “criteria tree” and the use of multi-criteria evaluation methodology.

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2. Evaluation criteria and preference tuning parameters in the DSS 2.0 system

The construction of the MLP model for assessing the utility of decision problems based on me-thodical solutions of the DSS 2.0 system, by Becker J., Budziski R. [2]. In this package you can, among others, carry out the assessments of the utility (classification) with the participation of dif-ferent methods of reproduction. In the case of MLP tasks (discussed below), the construction of the applied models is partially automated by the DSS 2.0 system (see: fig. 2).

Figure 2. The general form of the DSS 2.0 system with the specification of mapping methods

Source: own study.

The developed model should be supplemented with technical and economic parameters specific for the ontology and assessment criteria. It is an important problem for each cause and effect analysis or the multi-criteria optimisation. In the study of the criteria tree (criteria – sub-criteria – questions) the study guidelines were used [16]. As a result, the set of criteria and sub-criteria is created, which creates the “criteria tree” with the adaptive structure, what is shown in fig. 3.

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Figure 3. Model of criteria parameters in the language utility assessment

Source: own study.

Fig. 2 shows the specification of criteria and sub-criteria with the tuning parameters, i.e., trans-mitting weighs for the purposes of interpretation and decision. If the criteria are composed of criteria, they should be granted the appropriate weight (P) due to the fact that the ranks of sub-criteria are usually not equal. This process is called tuning of the sub-criteria tree. While the preferences for criteria (F) are transitive and we use them in case of arraying solutions by different users (with different preferences). In the present case, the preferences were assumed using the AHP method (Analytic Hierarchy Process) [12]. The OZM vector, placed in fig. 4, is the same as the dependent

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variable in the econometric analysis or the decision attribute in the induction of decision rules based on the approximate sets.

Figure4. Integrated partial criteria in the ontology utility assessment

Source: own study – system DSS2, Polish language version.

In the overall system we have a set of criteria (and sub-criteria) related to the decision attribute. Models with the utility function are most often characterised by different values of parameters at-tributed to criteria in the form of weighs, what is illustrated by the “Preferences” option. These weighs reflect the user’s preferences in achieving the objectives (targeted programming). While other approaches are not negated, e.g., threshold restrictions. It is about a deliberate choice of criteria for the purposes of the intended model studies.

3. Multi-criteria optimisation in the utility assessment

In the adopted MLP methodology (see: Multi-criteria linear programming) there is a phenome-non of competitiveness, where the increase of the degree of implementation of one of the goals entails a reduction of the degree of implementation of other goals. In this situation, an important step in the process of supporting decision is to determine the way of proceeding (method selection) lead-ing to obtainlead-ing the solution, which is better than others. This option examined two cases of multi-criteria optimisation; decision solutions of the decision-maker and supporting the beneficiaries in problems appealing to the disposer solutions. In the first case we are looking for solutions that meet the expectations of the disposer. While in the second one, all those solutions, which “were not in-cluded” in the area of the acceptable solutions for searching the “cheapest” way for finding the

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solutions in the collection, which are accepted by the disposer; this solution allows for meeting the functioning condition, called reverse auctions or benchmarking, where we equate to the best so-lutions.

The above problem will be considered mathematically; for multi-criteria tasks on the decision set X, we should specify several functionals

¦

= = s j kj j k x d x f 1 ) ( for k = 1, 2, …, r, (1)

which are optimised with respect to certain limits ddk for k = 1, 2, …, r, (e.g. with respect to preset targets to be achieved) and with constraints:

• local – appropriate for the given object (offer, request)

i s j ij j bb x b ≥= ≤ =

¦

1 , i = 1, 2, …, m and xj6 0, j = 1, 2, …, s, (2)

common – appropriate for all models (offers, requests)

i s j ij j cc x c ≥= ≤ =

¦

1 , i = 1, 2, …, m and xj6 0, j = 1, 2, …, s, (3)

where: xj are decision variables, and dkj, bij and bbi are the known task constants. These functionals convert the decision set X into the criteria space f(x) ⊂ Rk, where there is no natural linear order, and the set f(x) can be ordered in many ways. Different ordering of the space Rk most often come with a different decision hierarchy on the set X and a different solution to the task. The approach that does not require the a priori determination of the value of the goals to be implemented, based on the “target game” axiom, the difference of non-negative quality indicators qk – beneficial traits and pk – undesirable traits for k = 1, 2, r, were proposed by R. Budziski (1988). This method reduces the preferred conditions (the synthesis of the selected limitations and balances of the task is done) to the form of the target function (utility function):

¦

=

¦

=

= = r k k k k k r k k

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q

u

a

d

f

d

F

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Where in a1, a2, …, ar are the ranks of significance (preferences) applied to achieve different

objectives. While uk are technical parameters bringing the k-th sub-goals down to their equal weight in the optimisation calculations:

¦

= = n t kj k p q k d l u 1 , 100 (5)

where: are absolute values of technical and economic parameters standing in the equations of partial goals with j-th decision variables, and lk is the number of non-zero elements adopted for calculations, in the k-th row of partial goals. Then, with their participation, each solution is assessed

kj d

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with many quality indicators. The idea of the task is relatively simple, if the user possesses the basic knowledge of the structure of the linear programming tasks. [3] The above formalisation is derived from the method of goal programming, in which the exceeding and/or lack of achievement of the goal string is minimised: from the a priori preset values. One virtual variable was introduced in the place of “exceeding” and “lack of achievement” variables, which maximises (monitors) the acquired indicators of quality assessment of the optimised criteria structures.

The DSS 2.0 system with the benchmarking procedure creates a unique reference procedure for the selected objects (applications, models, classification solutions). The procedure is three-step: de-fining the best objects, simulation and reference correction of the object and the verification of the primary solution, where a new solution is shaped. Actions for the specific objects can be repeated many times. In the present case, the assessments of the ontology languages utility, we strive for the determination of the correction of the criterion parameters, which will allow the improvement of the rejected solutions investment (fig. 5).

Figure 5. Ranking of language technologies in the benchmark procedure DSS 2.0

Source: own calculations in the DSS 2.0 system, Polish language version.

Fig. 5 presented the multi-criteria ranking with the assumed preferences3 and global condition,

in which the selection of 3 best language technologies was declared. These are: Ontolingua − 4.53, LOOM – 4.00 and OWL_2FULL − 3.93 FMLP. The others form the so-called rejected solutions.

Among them, we are interested by the Flogic technology = 3.73 FMLP, which was on the 5th place.

The further proceeding involves: the assessment "to what extent does the rejected object have to

change its criterion parameters, so that it is among the best". This corresponds to the discussed

option, which has the possibility to change the ranking of objects and to study their competitiveness in relation to other objects.

3 The user has shown preferences with the AHP method (in %): Concepts D

1 = 0.30, Taxonomies D2 = 0.19, Relations D3 =

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Figure 6. Simplified reference proceeding in optimisation

Source: own study.

Model parameters can be changed “manually” or through the system (automatically). The

simu-lation option is a research procedure, where the change of the object parameters, sending its data to

the window “A”, optimisation together with the objects data from the window “B” leads to the study of competitiveness of the “new proposal” obtained from the simulation in relation to “old solutions” (fig. 6). It is an interesting idea for a new group of decision support systems based on the so-called reverse auctions, where there is the phenomenon of competitiveness in the access to the distributed assets. The applied simulation option is based on the criterion vector, which level is obtained in a special procedure (fig. 7).

Figure 7. Simulation procedure in the study of the competitiveness of objects

Source: own study based on [2].

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The simulation algorithm was based on altering the criteria parameters in the adopted validation ranges for each sub-target separately. The objects, criteria and the method of simulation study are selected individually, what is shown in fig 7.

Figure 8. Results of the simulation utility study of the ontology language technologies

Source: own calculations in the DSS 2.0 system, Polish language version.

The optimisation “ends” when the considered sub-block is in the group of the best solutions. The above procedure can be performed repeatedly, until obtaining the validation range boundaries in all objects. There may be cases, where such a solution is not obtained, e.g., due to the previously im-plemented threshold limitations. This means that the considered case is not competitive to the com-pared best objects (fig. 5, objects in window B). The simulation may cover not only the criteria parameters, but each technical and economic parameters of the decision task.

4. Conclusions

The aim of the studies undertaken and described in the article was to assess the utility of the knowledge representation languages with the MLP method. It presented the ranking of languages based on the assessment in the form of MLP utility functions with preference attributes specified with the AHP method of Prof. T. L. Saaty [12]. At the same time, it has shown the possibility of simulation and improvement of attribute properties of the selected language, characterised by the specific applicability in the construction of the domain ontologies. In the present case, simulation was applied to the selected partial criteria for the FLogic (Frame Logic) language technology.

In the benchmarking studies D06 (semantics) was deliberately omitted. It has been shown that the FLogic language (FMLP = 3.73) occupying the 5th place can be found among top 3, but it has

to improve the criteria parameters (e.g. like in fig. 8) and obtain the utility function index FMLP =

3.93, eliminating the OWL_2FULL technology from the platform, which had the result of FMLP =

3.92.

The article has also presented the rationale for the use of ontologies as the knowledge represen-tation, the features of individual knowledge representation languages were shown and their assess-ment was studied. Ontologies, including the domain ones, can be built using different formalisms

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and languages. The selection of the appropriate language that meets the requirements in the con-struction of the selected domain ontology, while taking into account the expert’s preferences from this field, requires the use of methods, among which the presented MLP method fulfils the conditions of the utility assessment of the technology of language ontologies to the satisfactory degree. Bibliography

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OCENA UĩYTECZNOĝCI JĉZYKÓW REPREZENTACJI WIEDZY W ONTOLOGIACH DZIEDZINOWYCH METODĄ WPL4

Streszczenie

Artykuł obejmuje problematyk jzyków reprezentacji wiedzy w ontologiach dzie-dzinowych: LOOM, OCML, OWL, FLogic, SHOE, RDF(S), Ontolingua, oraz OWL2. Celem podjtych i opisanych bada jest ocena uytecznoci tych jzyków przy uyciu metody WPL oraz moliwo poprawy właciwoci wybranego jzyka, który charak-teryzuje si wysok stosowalnoci w budowie ontologii dziedzinowych.

Słowa kluczowe: reprezentacja wiedzy, wpl, ahp, ontologia, baza wiedzy

Ryszard Budziski Waldemar Wolski University of Szczecin

Faculty of Economics and Management e-mail: wwolski@uoo.univ.szczecin.pl ryszard.budzinski@wneiz.pl Jarosław Becker

Paweł Ziemba

The Jacob of Parady University in Gorzów Wielkopolski The Department of Technology

e-mail: jbecker@ajp.edu.pl pziemba@ajp.edu.pl

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