Editing Web Ontology Language (section)

===OWL dialects===
The W3C-endorsed OWL specification includes the definition of three variants of OWL, with different levels of expressiveness. These are OWL Lite, OWL DL and OWL Full (ordered by increasing expressiveness). Each of these [[sublanguage]]s is a syntactic extension of its simpler predecessor. The following set of relations hold. Their inverses do not.

* Every legal OWL Lite ontology is a legal OWL DL ontology.
* Every legal OWL DL ontology is a legal OWL Full ontology.
* Every valid OWL Lite conclusion is a valid OWL DL conclusion.
* Every valid OWL DL conclusion is a valid OWL Full conclusion.

====OWL Lite====
OWL Lite was originally intended to support those users primarily needing a classification hierarchy and simple constraints. For example, while it supports [[cardinality]] constraints, it only permits cardinality values of 0 or 1. It was hoped that it would be simpler to provide tool support for OWL Lite than its more expressive relatives, allowing quick migration path for systems using [[Thesaurus|thesauri]] and other [[Taxonomy (general)|taxonomies]]. In practice, however, most of the expressiveness constraints placed on OWL Lite amount to little more than syntactic inconveniences: most of the constructs available in OWL DL can be built using complex combinations of OWL Lite features, and is equally expressive as the [[description logic]] <math>\mathcal{SHIF}(\mathbf{D})</math>.<ref name="grau.2008" /> Development of OWL Lite tools has thus proven to be almost as difficult as development of tools for OWL DL, and OWL Lite is not widely used.<ref name="grau.2008" />

====OWL DL====
OWL DL is designed to provide the maximum expressiveness possible while retaining computational [[Complete theory|completeness]] (either φ or ¬φ holds), [[Decidability (logic)|decidability]] (there is an effective procedure to determine whether φ is derivable or not), and the availability of practical reasoning algorithms. OWL DL includes all OWL language constructs, but they can be used only under certain restrictions (for example, number restrictions may not be placed upon properties which are declared to be transitive; and while a class may be a subclass of many classes, a class cannot be an instance of another class). OWL DL is so named due to its correspondence with [[description logic]], a field of research that has studied the logics that form the formal foundation of OWL.

This one can be expressed as <math>\mathcal{SHOIN}(\mathbf{D})</math>, using the letters logic above.

====OWL Full====
OWL Full is based on a different semantics from OWL Lite or OWL DL, and was designed to preserve some compatibility with RDF Schema. For example, in OWL Full a class can be treated simultaneously as a collection of individuals and as an individual in its own right; this is not permitted in OWL DL. OWL Full allows an ontology to augment the meaning of the pre-defined (RDF or OWL) vocabulary. OWL Full is undecidable, so no reasoning software is able to perform complete reasoning for it.