Description Logic: Fundamentals and Applications

By Fouad Sabry

What Is Description Logic

A family of formal knowledge representation languages known as description logics (DL) has been developed. A good number of DLs have a higher level of expressiveness than propositional logic but a lower level than first-order logic. On the other hand, the key reasoning issues for DLs are (typically) decidable, and efficient decision processes have been proposed and implemented for these problems. In contrast, the latter difficulties cannot be solved by reasoning at all. There is a general description logic, as well as a spatial description logic, a temporal description logic, a spatiotemporal description logic, and a fuzzy description logic. Each description logic strikes a unique balance between the expressive capability and the reasoning complexity that it offers by supporting a unique collection of mathematical constructors.

How You Will Benefit

(I) Insights, and validations about the following topics:

Chapter 1: Description Logic

Chapter 2: Knowledge Representation and Reasoning

Chapter 3: Semantic Web

Chapter 4: Ontology Inference Layer

Chapter 5: Web Ontology Language

Chapter 6: Semantic Technology

Chapter 7: Expressive Power (Computer Science)

Chapter 8: F-Logic

Chapter 9: Semantic Web Rule Language

Chapter 10: Ontology Engineering

(II) Answering the public top questions about description logic.

(III) Real world examples for the usage of description logic in many fields.

(IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of description logic' technologies.

Who This Book Is For

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of description logic.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: Jun 26, 2023

Book preview

Chapter 1: Description logic

A family of formal knowledge representation languages is known as description logics (DL). Numerous DLs are less expressive than first-order logic but more expressive than propositional logic. In contrast to the latter, efficient decision methods have been developed and implemented for the key reasoning issues faced by DLs, which are typically solvable. Each description logic supports a different set of mathematical constructs and has a unique balance between expressive strength and reasoning complexity. There are general, spatial, temporal, spatiotemporal, and fuzzy description logics.

Artificial intelligence employs DLs to explain and rationalize the pertinent concepts of an application domain (known as terminological knowledge). The Web Ontology Language (OWL) and its profiles are built on DLs, making it particularly significant in providing a logical framework for ontologies and the Semantic Web. In biomedical informatics, where DL helps to codify biomedical knowledge, is where DLs and OWL are most often used.

A description logic (DL) model represents ideas, functions, and interactions between people.

The axiom, a logical statement connecting roles and/or concepts, is the core modeling concept of a DL.

For concepts that are operationally comparable, the description logic community employs different nomenclature from the first-order logic (FOL) community; a few instances are shown below. Once more using alternative nomenclature, the Web Ontology Language (OWL) is listed in the table below.

There are numerous types of description logics, and there is an unofficial naming scheme that approximately characterizes the permitted operators. The name for a logic beginning with one of the following fundamental logics contains the expressivity:

any of the aforementioned extensions might come next:

Several canonical DLs don't quite adhere to this pattern, including:

For illustration, {\mathcal {ALC}} is a centrally important description logic from which comparisons with other varieties can be made.

{\mathcal {ALC}} is simply {\mathcal {AL}} with complement of any concept allowed, not only atomic ideas.

{\mathcal {ALC}} is used instead of the equivalent {\mathcal {ALUE}} .

Another illustration, the description logic {\mathcal {SHIQ}} is the logic {\mathcal {ALC}} plus extended cardinality restrictions, and inverse, transitive, and roles.

The naming conventions aren't purely systematic so that the logic {\mathcal {ALCOIN}} might be referred to as {\mathcal {ALCNIO}} and other abbreviations are also made where possible.

The Protégé ontology editor supports {\mathcal {SHOIN}}^{{\mathcal {(D)}}} .

three main terminology frameworks for biomedical informatics, SNOMED CT, GALEN, and GO, are expressible in {\mathcal {EL}} (with additional role properties).

OWL 2 provides the expressiveness of {\mathcal {SROIQ}}^{{\mathcal {(D)}}} , OWL-DL is based on {\mathcal {SHOIN}}^{{\mathcal {(D)}}} , and for OWL-Lite it is {\mathcal {SHIF}}^{{\mathcal {(D)}}} .

In the 1980s, description logic received its current nomenclature. Its previous names, in chronological order, were terminological systems and concept languages.

Formal (logic-based) semantics are absent from frames and semantic networks. KAON 2, CEL (2005), and RACER (2001) (2005).

Analytic tableaux is a method that is implemented by DL reasoners like FaCT and FaCT++. Algorithms that convert a SHIQ(D) knowledge base into a disjunctive datalog program are used to implement KAON2.

Syntactic versions of DL can be seen in the DARPA Agent Markup Language (DAML) and Ontology Inference Layer (OIL) ontology languages for the Semantic Web.

In particular, the formal semantics and reasoning in OIL use the {\mathcal {SHIQ}} DL.

recommendation.

The design of OWL is based on the {\mathcal {SH}} family of DL with OWL DL and OWL Lite based on {\mathcal {SHOIN}}^{{\mathcal {(D)}}} and {\mathcal {SHIF}}^{{\mathcal {(D)}}} respectively.

OWL2 is based on the description logic {\mathcal {SROIQ}}^{{\mathcal {(D)}}} .

In DL, the so-called TBox (terminological box) and the ABox are distinguished from one another (assertional box). The TBox typically contains sentences explaining idea hierarchies (i.e., relationships between concepts), whereas the ABox typically contains ground statements indicating where individuals fit in the hierarchy (i.e., relations between individuals and concepts). For instance, the claim:

is appropriate for the TBox, however the assertion:

has a place in the ABox.

In the same way that the two kinds of sentences are not treated differently in first-order logic, it is important to note that the TBox/ABox distinction is not significant (which subsumes most DL). A subsumption axiom like (1) is only a conditional restriction to unary predicates (concepts) with just variables appearing in it when it is translated into first-order logic. It is obvious that a statement in this format is not superior to sentences that solely contain constants (also known as grounded values) (2).

Therefore, why was the differentiation made? The division can be helpful when defining and designing decision-procedures for diverse DL, which is the main justification. Because certain important inference issues are linked to one but not the other (classification is related to the TBox, whilst instance checking is related to the ABox), a reasoner can, for instance, process the TBox and ABox separately. Another illustration is how, independently of the ABox, the complexity of the TBox can have a significant impact on how well a certain decision-procedure performs for a specific DL. Consequently, it is helpful to have a mechanism to discuss that particular area of the knowledge base.

The distinction can make sense from the viewpoint of the knowledge base modeler, which is the secondary justification. It is reasonable to distinguish between specific manifestations of terms and concepts in the universe and how we conceptualize them (class axioms in the TBox) (instance assertions in the ABox). In the aforementioned example, it makes sense to reuse the TBox for several branches that do not utilize the same ABox when the hierarchy within a corporation is the same in every branch but the assignment to employees is different in every department (since there are other people working there).

There are two characteristics of description logic that most other data description formalisms do not share: The unique name assumption (UNA) and the closed-world assumption