Editing Web Ontology Language (section)

==Semantics==
{{main|Semantics of programming languages}}

===Relation to description logics===
OWL classes correspond to [[description logic]] (DL) ''concepts'', OWL properties to DL ''roles'', while ''individuals'' are called the same way in both the OWL and the DL terminology.<ref>{{cite book |last=Sikos |first=Leslie F. |date=2017 |title=Description Logics in Multimedia Reasoning |url=https://www.springer.com/us/book/9783319540658 |location=Cham |publisher=Springer International Publishing |isbn=978-3-319-54066-5 |doi=10.1007/978-3-319-54066-5 |s2cid=3180114 }}</ref>

{{blockquote|In the beginning, IS-A was quite simple. Today, however, there are almost as many meanings for this inheritance link as there are knowledge-representation systems.|[[Ronald J. Brachman]]|''What IS-A is and isn't''<ref>Brachman, Ronald J. (1983); ''What IS-A is and isn't: An analysis of taxonomic links in semantic networks'', IEEE Computer, vol. 16, no. 10, pp. 30-36</ref>}}

Early attempts to build large ontologies were plagued by a lack of clear definitions. Members of the OWL family have [[model theory|model theoretic]] formal semantics, and so have strong [[logic]]al foundations.

Description logics are a family of logics that are decidable fragments of [[first-order logic]] with attractive and well-understood computational properties. OWL DL and OWL Lite semantics are based on DLs.<ref>{{cite web |url=http://www.cs.man.ac.uk/~horrocks/Publications/download/2003/HoPa03c.pdf |first1=Ian |last1=Horrocks |first2=Peter F. |last2=Patel-Schneider |title=Reducing OWL Entailment to Description Logic Satisfiability }}</ref>
They combine a syntax for describing and exchanging ontologies, and formal semantics that gives them meaning. For example, OWL DL corresponds to the <math>\mathcal{SHOIN}^\mathcal{(D)}</math> description logic, while OWL 2 corresponds to the <math>\mathcal{SROIQ}^\mathcal{(D)}</math> logic.<ref>{{cite book |title=Foundations of Semantic Web Technologies |first1=Pascal |last1=Hitzler  |author-link1=Pascal Hitzler |first2=Markus |last2=Krötzsch |first3=Sebastian |last3=Rudolph |publisher=CRCPress |date=2009-08-25 |isbn=978-1-4200-9050-5 |url=http://www.semantic-web-book.org }}</ref> Sound, complete, terminating [[reasoner]]s (i.e. systems which are guaranteed to derive every consequence of the knowledge in an ontology) exist for these DLs.

===Relation to RDFS===
OWL Full is intended to be compatible with [[RDF Schema]] (RDFS), and to be capable of augmenting the meanings of existing [[Resource Description Framework]] (RDF) vocabulary.<ref>{{cite web |url=http://www.w3.org/TR/2004/REC-owl-features-20040210/ |title=OWL Web Ontology Language Overview |first1=Deborah |last1=McGuinness |author-link=Deborah McGuiness |first2=Frank |last2=van Harmelen |author-link2=Frank van Harmelen |date=2004-02-10 |work=W3C Recommendation for OWL, the Web Ontology Language |publisher=World Wide Web Consortium |access-date=18 April 2010}}</ref> A [[model theory]] describes the formal semantics for
RDF.<ref>{{cite web |url=http://www.w3.org/TR/2004/REC-rdf-mt-20040210/ |title=RDF Semantics |first=Patrick |last=Hayes |author-link=Patrick J. Hayes |date=2004-02-10 |work=Resource Description Framework |publisher=World Wide Web Consortium |access-date=18 April 2010 }}</ref> This interpretation provides the meaning of RDF and RDFS vocabulary. So, the meaning of OWL Full ontologies are defined by extension of the RDFS meaning, and OWL Full is a [[extension (model theory)|semantic extension]] of RDF.<ref>{{cite web |url=http://www.w3.org/TR/owl-semantics/rdfs.html |title=OWL Web Ontology Language Semantics and Abstract Syntax Section 5. RDF-Compatible Model-Theoretic Semantics |first1=Peter F. |last1=Patel-Schneider |first2=Patrick |last2=Hayes |first3=Ian |last3=Horrocks |date=2004-02-10 |work=W3C Recommendation for OWL, the Web Ontology Language |publisher=World Wide Web Consortium |access-date=18 April 2010 }}</ref>

===Open world assumption===
{{blockquote|[The closed] world assumption implies that everything we don't know is ''false'', while the open world assumption states that everything we don't know is ''undefined''.|Stefano Mazzocchi|''Closed World vs. Open World: the First Semantic Web Battle''<ref>{{cite web |url=http://www.betaversion.org/~stefano/linotype/news/91/ |title=Closed World vs. Open World: the First Semantic Web Battle |first=Stefano |last=Mazzocchi |author-link=Setfano Mazzocchi |date=2005-06-16 |access-date=27 April 2010 |archive-url=https://web.archive.org/web/20090624113015/http://www.betaversion.org/~stefano/linotype/news/91/ |archive-date=24 June 2009 }}</ref>}}

The languages in the OWL family use the [[open world assumption]]. Under the open world assumption, if a statement cannot be proven to be true with current knowledge, we cannot draw the conclusion that the statement is false.

====Contrast to other languages====
A [[relational database]] consists of sets of [[tuple]]s with the same [[Attribute (computing)|attribute]]s. [[SQL]] is a query and management language for relational databases. [[Prolog]] is a [[Logic programming|logical programming]] language. Both use the [[closed world assumption]].