**3.1 The description logics**

218 Semantics – Advances in Theories and Mathematical Models

(Bosche, et al., 2008). Other promising approaches have only been tested on limited and very simple examples, and it is equally difficult to predict how they would fare when faced with more complex and realistic data sets. For example, the semantic network methods for recognizing components using context work well for simple examples of hallways and barren, rectangular rooms (Cantzler, 2003), but how would they handle spaces with complex

The presented methods for survey modeling and object recognition rely on hand-coded knowledge about the domain. Concepts like "Signals are vertical" and "Signals intersect with the ground" are encoded either explicitly, through sets of rules, or implicitly, through the design of the algorithm. Such hard-coded, rule based approaches tend to be brittle and break down when tested in new and slightly different environments. Additionally, we can deduce that authors model the context but not the 3D processing algorithms, the geometry and the topology. Furthermore, it will be difficult in such a case to extend an algorithm with new rule or to modify the rules to work in new environments. To make it more flexible and efficient, and in contrast with the literature, we opt to use a new data structure labeled ontology. In fact, the last one presents a formal representation of knowledge by a set of concepts within a domain, and the relationships between those concepts. It is used to reason about the entities within that domain, and may be used to describe the domain where the basic strength of formal ontology is their ability to present knowledge within their taxonomy, relations and conditions, but also to reason in a logical way based on Description Logics DL concepts. Based on these observations, we predict that more standard and flexible representations of facility objects and more sophisticated guidance based algorithms for object detection instead of a standard one, by modeling algorithmical, geometrical and topological knowledge within an ontology structure will open the way to significant improvement in facility modeling capability and generality since it will allow as to create a more dynamic algorithm sequence for object detection based on object's geometries and to

The growth of the World Wide Web has been tremendous since its evolvement both in terms of the content and the technology. The first Web generation was mainly presentation based. They provided information through the Web pages but did not allow users to interact with them. In short, they contained read only information. Moreover, they were only text pages and do not contain multimedia data. These Web sites have higher dependency on the presentation languages like Hypertext Markup Languages (HTML) (Horrocks, et al., 2004). With the introduction of e**X**tensible**M**arkup**L**anguage (XML), the information within the pages became more structured. Those XML based pages could hold up the contents in more structured method but still lack the proper definition of semantics within the contents, (Berners-Lee, 1998). For this reason, the needs of intelligent systems which could exploit the wide range of information available within the Web are widely felt. Semantic Web is

The term "*Semantic Web*" is coined by Tim Berners-Lee in his work (Lee, et al., 2001) to propose the inclusion of semantic for better enabling machine-people cooperation for

geometries and clutter.

make more robust the identification process.

**3. Knowledge and Semantic web** 

envisaged to address this need.

**2.3 Discussion** 

Actually, the convergence of formal foundations for extensible, semantically understood structure within description logic and the overall usability targets of the predecessor of DL and the Web languages for broader usability of Web has led to the effort such as Ontology Interface Language (OIL) (Fensel, et al., 2001). It presents the first major effort to develop a language which has its base in Description Logic. It was a part of the broader project called On-To-Knowledge funded by European Union. This is the first time that the concept within ontology is explicitly used within a Web based environment. However, it did not completely leave out the primitives of frame base languages with the formal semantics and reasoning capabilities by including them within the language. The syntax of OIL is based on RDF and XML with their limitations to provide complete semantic foundations at that time. However, it has started a trend of mapping description logic within the Web based language for Semantic Web. It maps description logic through *SHIQ*. The derivation of *SHIQ* with respect to naming convention of the Description Logic is given as:

```
S: Used for all ALC with transitive roles R+ 
H: Role inclusion axioms R1⊑ R2 (is_component_of ⊑ is_part_of) 
I: Inverse Role R-(isPartOf = hasPart-) 
Q: Qualified number restrictions
```
#### **3.1.1 The base languages**

Complex descriptions can be built up through the above mentioned elementary descriptions of concepts and roles. These descriptions are given different notations over the time. The Attributive Language (*AL*) has been introduced in 1991 as minimal language that is of practical interest (Schmidt-Schauß, et al., 1991). It is further complemented through Attributive Concept Language with Complements (*ALC*) to allow any concepts or roles to be included and not just atomic concepts and atomic roles which were the previous elements of descriptions. *ALC* is the important notation format to express Description Logics. Fig 2 illustrates the syntax rules on describing the concept.

From Unstructured 3D Point Clouds to Structured Knowledge - A Semantics Approach 221

Description logics (DLs) are a family of logics which represents the structured knowledge. The Description Logic languages are knowledge representation languages that can be used to represent the knowledge of an application domain in a structured and formally wellunderstood way (McGuinness, et al., 2003), (Calvanese, et al., 2005). Description logics contain the formal, logic-based semantics, which present the major reason for its choice for Semantic Web languages over its predecessors. The reasoning capabilities within the DLs add a new dimension. Having these capabilities as central theme, inferring implicitly represented knowledge becomes possible. The movement of Description Logic into its applicability can be viewed in terms of its progression in Web environment (Noy, et al., 2001). Web languages such as XML or RDF(S) could benefit from the approach DL takes to formalize the structured knowledge representation (Lassila, 2007). This has laid background behind the emergence of Description Logic languages in Web. Actually, an agreement to encode these operators using an alphabetic letter to denote expressivity of DLs has seen the light. These letters in combinations are used to define the capabilities of DLs in terms of their performances. This implies to the DL languages as well. As could be seen in Fig 3, *ALC* has been extended to transitive role and given abbreviation S in the convention. Where S is used in every DL systems and languages as it plays significant role in shaping the

**3.1.2 The description logics formalization** 

behavioural nature of every DL systems.

*U* : Concept disjunction ��� : Existential quantification, ��� �

most 2 adult Children)

**3.2 The knowledge base** 

*I* :Inverse role R-, e.g isPartof=hasPart-*F* :functional role, e.g functional(hasAge) *R+* :Transitive role , e.g., transitive (isPartOf)

Fig. 3. Naming convention of Description Logic.

*AL* :�� � � �� � � � � � � � � �� � ��� � � ��� � *C* : Concept �������� ��. Thus, *ALC=AL+C S* : Used for *ALC* with transitive role R+

*H* : Role inclusions axioms, R1⊑ R2, e.g is\_component\_of ⊑ is\_part\_of

*O* :Nominals (singleton class), {a}. e.g ����\_������ �������

*N* :Number Restrictions, (≥ nR) and (≤ nR), e.g (≥ has\_Child) (has at least 3 child)

*R* :role inclusion with comparison, R1 o R2 ⊑ S, e.g, isPartOf o isPartOf ⊑ ��������

Description Logics supports serialization through the human readable forms of the real world scenario with the classification of concepts and individuals. Moreover, they support the hierarchical structure of concepts in forms of subconcepts/superconcepts relationships of a concept between the concepts of a given terminology. This hierarchical structure provides efficient inference through the proper relations between different concepts. The individual-concept relationship could be compared to instantiation of an object to its class in object-oriented concept. In this manner, the approach DL takes can be related to classification of objects in a real world scenario. Description logics provide a formalization

*Q* :Qualified number restriction, (≥n R.C) and (≤n R.C) , e.g (≤2 has\_child.Adult) (has at


Here C and D are concept description and R is role

Fig. 2. The syntax and semantics based on *ALC.*

We introduce in this section the terminological axioms, which make statements about how concepts or roles are related to each other. Then we single out definitions as specific axioms and identify terminologies as sets of definitions by which we can introduce atomic concepts as abbreviations or names for complex concepts. In the most general case, terminological axioms have the form �� � ��� �� � ������ � �� � � � where C, D are concepts (and R, S are roles). Axioms of the first kind are called inclusions, while axioms of the second kind are called equalities. An equality whose left-hand side is an atomic concept. It´s used to introduce symbolic names for complex descriptions e,g. ���������� � ������� ⊓ ∃�������� ��������. It could be clearly seen within Fig 2 that these concept descriptions are built with the concept constructors. The first four constructors are not dependent on the roles whereas the last two utilizes the roles in the constructors. This dependency is called role restrictions. Formally, a role restriction is an unnamed class containing all individuals that satisfy the restriction. DLs expressed through *ALC* provide two such restrictions in Quantifier restriction and value restrictions.

#### **The Quantifier restriction**

It´s again classified as the **existential quantifier** (at least one, or some) and **universal quantifiers** (every).

The existential quantifier links a restriction concept to a concept description or a data range. This restriction describes the unnamed concept for which there should be at least one instance of the concept description or value of the data value. Simplifying, the property restriction *P* relates to a concept of individuals *x* having at least one y which is either an instance of concept description or a value of data range so that *P(x,y)* is an instance of *P*.

From the other side, the **universal quantifier** () (*every)* constraint links a restriction concept to a concept description or a data range. This restriction describes the unnamed concept for which there should all instances of the concept description or value of the data value. Simplifying, the property restriction *P* relates to a concept of individuals *x* having all y which is either an instance of the concept description or a value of data range so that *P(x,y)*  is concidered as an instance of *P*.

#### **The Value restriction**

It links a restriction concept directly to a value which could be either an individual or data value.
