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pl:miw:piw08_hekateonto:description_logics [2017/07/17 10:08] |
pl:miw:piw08_hekateonto:description_logics [2019/06/27 15:50] (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. | ||
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| + | 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. | ||
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| + | 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. | ||
