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Description logic was designed as an extension to Frame s and Semantic Network s, which were not equipped with formal logic-based semantics. Description logic was given its current name in the 1980s . Previous to this it was called (chronologically): ''terminological systems'', and ''concept languages''. Today description logic has become a cornerstone of the Semantic Web for its use in the design of Ontologies . The OWL-DL and OWL-Lite sub-languages of the W3C -endorsed Web Ontology Language (OWL) are based on a description logic. The first DL-based system was KL-ONE (by Brachman and Schmolze, 1985). Some other DL systems came later. They are LOOM (1987), BACK (1988), KRIS (1991), CLASSIC (1991), FaCT (1998) and lately RACER (2001), CEL (2005), and KAON 2 (2005). SYNTAX Syntax of description logics consists of
In description logics, concept names are regarded as atomic concepts, role names are regarded as atomic roles. In general, a concept denotes the set of individuals that belongs to it, and a role denotes a relationship between concepts. The syntax of a member of the description logic family is characterized by its recursive definition, in which the constructors that can be used to form concept terms are stated. Some common constructors include logical constructors in First-order Logic such as ''intersection'' or ''conjunction'' of concepts, ''union'' or ''disjunction'' of concepts, ''negation'' or ''complement'' of concepts, ''value restriction'' (''universal restriction''), ''existential restriction'', etc. Other constructors may also include restrictions on roles which are usual for binary relations, for example, inverse, transitivity, functionality, etc. Especially for intersection and union, description logics use the symbols and to distinguish them from the first-order logic and . The following is an example of definition of the syntax of the description logic AL.
For example, is an AL-concept, but is not. Also, is an AL-concept, but is not. SEMANTICS The semantics of description logics is defined by interpreting concepts as sets of individuals and roles as sets of pairs of individuals. Those individuals are typically assumed from a given domain. The semantics of non atomic concepts and roles is then defined in terms of atomic concepts and roles. This is done by using a recursive definition similar to the syntax. For example, given a set as the domain, an interpretation of AL-concepts is defined first over atomic concepts and roles as follows:
Next, this interpretation is extended to non atomic concept and role according to the constructors. This is done in the following.
Thus, according to the way concepts and roles interpreted above, if P is interpreted as the set of all persons and F is interpreted as the set of all female, then the set of all persons that are not female can be expressed by the concept : MODELLING IN DESCRIPTION LOGICS In DLs, a distinction is drawn between the so-called TBox (terminological box) and the ABox (assertional box). In general, the TBox contains sentences describing concept hierarchies (i.e., Relation s between Concept s) while the ABox contains "ground" sentences stating where in the hierarchy individuals belong (i.e., relations between individuals and concepts). For example, the statement: (1) Every employee is a person belongs in the TBox, while the statement: (2) Bob is an employee belongs in the ABox. Note that the TBox/ABox distinction is not significant, in the same sense that the two "kinds" of sentences are not treated differently in first-order logic (which subsumes most DLs). When translated into first-order logic, a subsumption Axiom like (1) is simply a conditional restriction to Unary Predicate s (concepts) with only variables appearing in it. Clearly, a sentence of this form is not privileged or special over sentences in which only constants ("grounded" values) appear like (2). So why was the distinction introduced? The primary reason is that the separation can be useful when describing and formulating decision-procedures for various DLs. For example, a reasoner might process the TBox and ABox separately, in part because certain key inference problems are tied to one but not the other one ('classification' is related to the TBox, 'instance checking' to the ABox). Another example is that the complexity of the TBox can greatly affect the performance of a given decision-procedure for a certain DL, independently of the ABox. Thus, it is useful to have a way to talk about that specific part of the Knowledge Base . The secondary reason is that the distinction can make sense from the knowledge base modeller's perspective. It is plausible to distinguish between our conception of terms/concepts in the world (class axioms in the TBox) and particular manifestations of those terms/concepts (instance assertions in the ABox.) FUZZY DESCRIPTION LOGICS Main article: Fuzzy Description Logics Fuzzy description logic combines Fuzzy Logic with DLs. Since many concepts that are needed for Intelligent Systems lack well defined boundaries, or precisely defined criteria of membership, we need fuzzy logic to deal with notions of vageness and imprecision. This offers a motivation for a generalisation of description logics towards dealing with imprecise and vague concepts. DIFFERENCES WITH OWL Terminology A ''concept'' in DL jargon is referred to as a ''class'' in OWL. A ''role'' in DL jargon is a ''property'' in OWL. Names Should add discussion of Unique Name Assumption (UNA) versus no unique name assumption. OWL does not make the UNA. DL EXPRESSIVITY Description Logic expressivity is denoted as follows. The Protégé ontology editor supports . OWL-DL provides the expressiveness of , and OWL 1.1 is based on . DESCRIPTION LOGIC REASONERS There are some Reasoner s to deal with OWL and Description Logics. These are some of the most popular:
DL reasoners, such as FaCT, FaCT++, RACER, DLP and Pellet,implement the Analytic Tableau Method . KAON2 is implemented by algorithms which reduce a SHIQ(D) knowledge base to a disjunctive Datalog program. Other tools related to Description Logics include the following:
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