would a semantics by any other name look as formal?

EXECUTIVE SUMMARY:  

  The RDF-Based Semantics document should use "RDF-based semantics"
  uniformly when talking about the semantics that it defines.



From: "Michael Schneider" <schneid@fzi.de>
Subject: RE: LC responses 28, 48 & 58
Date: Tue, 10 Mar 2009 23:48:41 +0100

> In the proposed answer to LC28
> 
>   <http://www.w3.org/2007/OWL/wiki/LC_Responses/FH2>
> 
> it is stated:
> 
> [[
> OWL 2 separates syntax from semantics, and that OWL 2 Full, 
> DL, QL, EL and RL are all refer to syntactic variants, 
> ]]
> 
> Frankly, this makes no sense to me. OWL 2 Full is certainly not a "syntactic
> variant", just as OWL 1 Full hasn't been.
> 
> In the OWL 1 Full spec, there existed semantic-related terms like "OWL Full
> interpretation" and "OWL Full entails". And OWL Full was characterized as
> follows in a semantic way:
>  
> <http://www.w3.org/TR/owl-semantics/rdfs.html#5.3>
> [[
> OWL Full augments the common conditions with conditions 
> that force the parts of the OWL universe 
> to be the same as their analogues in RDF.
> [...]
> ]]
> 
> With this in mind, in the RDF-Based Semantics document I have used the term
> "OWL 2 Full" exclusively to mean the /semantics/. 

I do not believe that "OWL Full" ever meant just the semantics.  My
recollection is that "OWL Full" was always the combination of syntax and
semantics.  However, getting *normative* guidance on the precise
definitions is rather difficult.  Many of the excerpts below are from
non-normative documents or document sections, and the quotes from
normative sections are not about OWL, but instead about some aspect of
OWL.



>From OWL S&AS:

This description of OWL, the Web Ontology Language being designed by the
W3C Web Ontology Working Group, contains a high-level abstract syntax
for both OWL DL and OWL Lite, sublanguages of OWL. A model-theoretic
semantics is given to provide a formal meaning for OWL ontologies
written in this abstract syntax. A model-theoretic semantics in the form
of an extension to the RDF semantics is also given to provide a formal
meaning for OWL ontologies as RDF graphs (OWL Full). A mapping from the
abstract syntax to RDF graphs is given and the two model theories are
shown to have the same consequences on OWL ontologies that can be
written in the abstract syntax. 

This document contains several interrelated normative specifications of
the several styles of OWL, the Web Ontology Language being produced by
the W3C Web Ontology Working Group (WebOnt). First, Section 2 contains a
high-level, abstract syntax for both OWL Lite, a subset of OWL, and OWL
DL, a fuller style of using OWL but one that still places some
limitations on how OWL ontologies are constructed. Eliminating these
limitations results in the full OWL language, called OWL Full, which has
the same syntax as RDF. The normative exchange syntax for OWL is RDF/XML
[RDF Syntax]; the OWL Reference document [OWL Reference] shows how the
RDF syntax is used in OWL. A mapping from the OWL abstract syntax to RDF
graphs [RDF Concepts] is, however, provided in Section 4. 

This document contains two formal semantics for OWL. One of these
semantics, defined in Section 3, is a direct, standard model-theoretic
semantics for OWL ontologies written in the abstract syntax. The other,
defined in Section 5, is a vocabulary extension of the RDF semantics
[RDF Semantics] that provides semantics for OWL ontologies in the form
of RDF graphs. Two versions of this second semantics are provided, one
that corresponds more closely to the direct semantics (and is thus a
semantics for OWL DL) and one that can be used in cases where classes
need to be treated as individuals or other situations that cannot be
handled in the abstract syntax (and is thus a semantics for OWL
Full). These two versions are actually very close, only differing in how
they divide up the domain of discourse. 

Appendix A contains a proof that the direct and RDFS-compatible
semantics have the same consequences on OWL ontologies that correspond
to abstract OWL ontologies that separate OWL individuals, OWL classes,
OWL properties, and the RDF, RDFS, and OWL structural
vocabulary. Appendix A also contains the sketch of a proof that the
entailments in the RDFS-compatible semantics for OWL Full include all
the entailments in the RDFS-compatible semantics for OWL DL. Finally a
few examples of the various concepts defined in the document are
presented in Appendix B. 

There are two different styles of using OWL. In the more free-wheeling
style, called OWL Full, the three parts of the OWL universe are
identified with their RDF counterparts, namely the class extensions of
rdfs:Resource, rdfs:Class, and rdf:Property. In OWL Full, as in RDF,
elements of the OWL universe can be both an individual and a class, or,
in fact, even an individual, a class, and a property. In the more
restrictive style, called OWL DL here, the three parts are different
from their RDF counterparts and, moreover, pairwise disjoint. The
more-restrictive OWL DL style gives up some expressive power in return
for decidability of entailment. Both styles of OWL provide entailments
that are missing in a naive translation of the DAML+OIL model-theoretic
semantics into the RDF semantics. 

The semantics of OWL DL and OWL Full are very similar. The common
portion of their semantics is thus given first, and the differences left
until later. 

>From OWL Ref 

As also discussed in the OWL Overview document [OWL Overview], and
subsequently the OWL Guide [OWL Guide], the OWL language provides two
specific subsets that we believe will be of use to implementors and
language users. OWL Lite was designed for easy implementation and to
provide users with a functional subset that will get them started in the
use of OWL. OWL DL (where DL stands for "Description Logic") was
designed to support the existing Description Logic business segment and
to provide a language subset that has desirable computational properties
for reasoning systems. The complete OWL language (called OWL Full to
distinguish it from the subsets) relaxes some of the constraints on OWL
DL so as to make available features which may be of use to many database
and knowledge representation systems, but which violate the constraints
of Description Logic reasoners.

NOTE: RDF documents will generally be in OWL Full, unless they are
specifically constructed to be in OWL DL or Lite.

OWL Full and OWL DL support the same set of OWL language
constructs. Their difference lies in restrictions on the use of some of
those features and on the use of RDF features. OWL Full allows free
mixing of OWL with RDF Schema and, like RDF Schema, does not enforce a
strict separation of classes, properties, individuals and data
values. OWL DL puts constraints on the mixing with RDF and requires
disjointness of classes, properties, individuals and data values. The
main reason for having the OWL DL sublanguage is that tool builders have
developed powerful reasoning systems which support ontologies
constrained by the restrictions required for OWL DL. For the formal
definitions of the differences between OWL Full and OWL DL the reader is
referred to the Semantics and Abstract Syntax document [OWL
S&AS]. Sec. 8.2 "OWL DL" summarizes the differences between OWL Full and
OWL DL.

OWL Lite is a sublanguage of OWL DL that supports only a subset of the
OWL language constructs. OWL Lite is particularly targeted at tool
builders, who want to support OWL, but want to start with a relatively
simple basic set of language features. OWL Lite abides by the same
semantic restrictions as OWL DL, allowing reasoning engines to guarantee
certain desirable properties. A summary of the language constructs
allowed in OWL Lite is given in Sec. 8.3. For a more formal description
of the subset of OWL language constructs supported by OWL Lite the
reader is referred to the Semantics and Abstract Syntax document [OWL
S&AS].

NOTE: RDF users upgrading to OWL should be aware that OWL Lite is not
simply an extension of RDF Schema. OWL Lite is a light version of OWL DL
and puts constraints on the use of the RDF vocabulary (e.g.,
disjointness of classes, properties, etc.). OWL Full is designed for
maximal RDF compatibility and is therefore the natural place to start
for RDF users. When opting for either OWL DL or OWL Lite one should
consider whether the advantages of OWL DL/Lite (e.g., reasoning support)
outweigh the DL/Lite restrictions on the use of OWL and RDF constructs.

NOTE: OWL Lite is defined in this document as a number of additional
restrictions on OWL DL. This mean that, OWL DL constructs are also part
of OWL Lite, unless explicitly stated otherwise. Sec. 8.3.provides a
summary of these additional OWL Lite restrictions.

>From OWL Overview

The OWL Web Ontology Language is designed for use by applications that
need to process the content of information instead of just presenting
information to humans. OWL facilitates greater machine interpretability
of Web content than that supported by XML, RDF, and RDF Schema (RDF-S)
by providing additional vocabulary along with a formal semantics. OWL
has three increasingly-expressive sublanguages: OWL Lite, OWL DL, and
OWL Full. 

OWL Full is meant for users who want maximum expressiveness and the
syntactic freedom of RDF with no computational guarantees. For example,
in OWL Full a class can be treated simultaneously as a collection of
individuals and as an individual in its own right. OWL Full allows an
ontology to augment the meaning of the pre-defined (RDF or OWL)
vocabulary. It is unlikely that any reasoning software will be able to
support complete reasoning for every feature of OWL Full. 

* 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.

 Ontology developers adopting OWL should consider which sublanguage best
 suits their needs. The choice between OWL Lite and OWL DL depends on
 the extent to which users require the more-expressive constructs
 provided by OWL DL. The choice between OWL DL and OWL Full mainly
 depends on the extent to which users require the meta-modeling
 facilities of RDF Schema (e.g. defining classes of classes, or
 attaching properties to classes). When using OWL Full as compared to
 OWL DL, reasoning support is less predictable since complete OWL Full
 implementations do not currently exist.
OWL Full can be viewed as an extension of RDF, while OWL Lite and OWL DL
 can be viewed as extensions of a restricted view of RDF. Every OWL
 (Lite, DL, Full) document is an RDF document, and every RDF document is
 an OWL Full document, but only some RDF documents will be a legal OWL
 Lite or OWL DL document. Because of this, some care has to be taken
 when a user wants to migrate an RDF document to OWL. When the
 expressiveness of OWL DL or OWL Lite is deemed appropriate, some
 precautions have to be taken to ensure that the original RDF document
 complies with the additional constraints imposed by OWL DL and OWL
 Lite. Among others, every URI that is used as a class name must be
 explicitly asserted to be of type owl:Class (and similarly for
 properties), every individual must be asserted to belong to at least
 one class (even if only owl:Thing), the URI's used for classes,
 properties and individuals must be mutually disjoint. The details of
 these and other constraints on OWL DL and OWL Lite are explained in
 appendix E of the OWL Reference. 

This section provides a quick index to all the language features for OWL
Lite, OWL DL, and OWL Full. 





[...]

I expect that it is best not to conflate OWL 2 Full with the RDF-Based
Semantics.  The Direct Semantics document is careful not to make this
conflation, and uses "Direct Semantics" or some variant thereof when
referring to its semantics.  I suggest that the RDF-Based Semantics
document go this way, and use "RDF-Based Semantics" when referring to
the semantics it defines.

> Best,
> Michael

peter

Received on Friday, 13 March 2009 23:51:44 UTC