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pl:miw:piw08_hekateonto:description_logics [2017/07/17 08:08] (aktualna)
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 +===== A few words about description logics =====
 +Some useful information (from http://​en.wikipedia.org/​wiki/​Description_logic)
  
 +==== Syntax ====
 +Syntax of description logics consists of
 +  * A set of unary predicate symbols that are used to denote concept names;
 +  * A set of binary relations that are used to denote role names;
 +  * A recursive definition for defining concept terms from concept names and role names using constructors.
 +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.
 +
 +==== 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:
 +  * An atomic concept is interpreted as a set of individuals that is a subset of the domain.
 +  * An atomic role is interpreted as a set of pairs of individuals from the domain, i.e., a binary relation over the domain. In this case, if an individual x is related to y via a role R, then y is called an R-successor of x.
 +
 +Next, this interpretation is extended to non atomic concept and role according to the constructors. This is done in the following.
 +  * The top concept is interpreted as the whole domain.
 +  * The bottom concept is interpreted as the empty set.
 +  * The interpretation of ¬C is the set of all individuals in the domain which does not belong to the interpretation of C.
 +  * Intersection of two concepts C and D is interpreted as set-intersection,​ i.e., the set of all individuals in the domain that belongs to both the interpretation of C and the interpretation of D.
 +  * The value restriction ∀R.C is interpreted as the set of all individuals in the domain whose R-successors (if any) all belong to the interpretation of C.
 +  * The limited existential restriction ∃R.Τ is interpreted as the set of all individuals in the domain that have at least one R-successor.
 +
 +==== TBox and ABox ====
 +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., **relations between concepts**) while the ABox contains "​ground"​ sentences stating where in the hierarchy individuals belong (i.e., **relations between individuals and concepts**).
 +
 +==== Differences with OWL ====
 +A concept in DL jargon is referred to as a class in OWL. A role in DL jargon is a property in OWL.
pl/miw/piw08_hekateonto/description_logics.txt · ostatnio zmienione: 2017/07/17 08:08 (edycja zewnętrzna)
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