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Initial comments on OWL 2 Full Semantics

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Tue, 02 Sep 2008 21:11:25 -0400 (EDT)
Message-Id: <20080902.211125.73660423.pfps@research.bell-labs.com>
To: schneid@fzi.de
Cc: public-owl-wg@w3.org, team-owl-chairs@w3.org

Here are my comments on the OWL 2 Full Semantics.    I haven't made
review comments because I read the document while I was not connected to
the web, and thus couldn't edit the document.

In general I think that the document is quite good.  I have a number of
minor changes listed here.

I also have a comment that is more general than the document itself:

- owl:distinctMembers should be deprecated, as its function is handled
  by owl:members

Initial comments on the document:

- Vocabulary changes
  xsd:short - add to list of datatypes
  xsd:anyURI - replace owl:anyURI by xsd:anyURI
  owl:NAryDatatype - remove
  owl:datatypeArity - remove
  owl:Annotation - add as class, subset of IR

- "owlV" is not used after being defined.  I suggest removing it from
  the definition of the OWL 2 Full vocabulary. 

- The deprecation of owl:DataRange should say
    The URI reference rdfs:Datatype SHOULD be used instead.

- Definition 3.2 should also require that the datatype and facet names
  of D be in V. 

- Definition 3.2 should read  "... let V be a vocabulary that includes

- What are the "constraints in this section" referred to in Definition
  3.2?  I don't see any. 

- Definition 3.3 and 3.4: Satisfaction of RDF graphs is not defined in
  this document.  If this means some RDF satisfaction, then you need to
  there.  If not, you need to define satisfaction.

- Definition 3.3:  Q is not used.

- The semantic conditions are additions to also the D-entailment
  conditions, I think.  The first sentence of Section 4 should be
  changed accordingly.

- ICEXT(owl:NamedIndividual) = IR is probably incorrect, there are only
  countably many named individuals, but potentially uncountably many
  resources.  Should be <= IR.

- Table 4.1 - add column for description, e.g., Domain of discourse /
  Literal Values / Ontologies / Classes / Datatypes / ...

- owl:NAryDatatype is no longer in the RDF mapping
  owl:datatypeArity is no longer in the RDF mapping

- Replace "<= empty set" with "= empty set" in several places.

- IEXT(IS(owl:object)) <= ICEXT(IS(owl:Axiom)) x IR is wrong, as it
  states that annotated annotations are axioms.  It should be IR x IR.
  Similarly for owl:predicate and owl:subject.  (This may be because the
  document does not yet handle annotations on annotations.)

- owl:allValuesFrom should be <= owl:Restriction x IC.

- owl:TopDataProperty has wrong domain.  It should be = IR x ILV.

- Table 4.7 needs to be augmented with the conditions for nary some/all
  as follows: 
  if l is the sequence p1,...,pn in IDP
  - <x,c> in IEXT(IS(owl:someValuesFrom))
    <x,l> in IEXT(IS(owl:onProperties))
    ICEXT(x) = { y | exists z1, ..., zn  <y,zi> in IEXT(pi) for each
                                         and <z1,...,zn> in ICEXT(c) }
  - <x,c> in IEXT(IS(owl:allValuesFrom))
    <x,l> in IEXT(IS(owl:onProperties))
    ICEXT(x) = { y | forall z1, ..., zn  <y,zi> in IEXT(pi) for each
                                         imply <z1,...,zn> in ICEXT(c) }

- The above change removes the need for Table 4.9.

- The last part of the paragraph before Table 4.10 should read something
    Note that only the additional semantic conditions are given here and
    that the other RDFS conditions on this vocabulary are retained. 

- There is no definition of sequence.

- Semantic conditions should be provided for property chains directly,
  as in:

  Table 4.11: Property Chains
   if l sequence of p1,...,pn in IR
      <x,l> in IEXT(IS(owl:propertyChain))
     x,p1,...pn in IP
     IEXT(x) = IEXT(p1) o ... o IEXT(pn) 

- The x,y,z in Table 4.15 should be explicitly quantified over IR in
  the RHS of the table.

- I believe that Table 4.16 should have x in CEXT(c), y in CEXT(c).
  Also Table 4.16 is missing quantifiers for the zi.  I believe that
  they should be existentially quantified.

- Table 4.18 is missing a membership symbol.

- Table 4.18 already almost handles annotations on annotations, I think,
  provided that the domain of the OWL reification properties are changed
  as suggested.  However, I think that it would be better to change
  Table 4.18 and its introduction as follows:

    Table 4.18 lists the semantic conditions for the OWL vocabulary used
    for some axiom annotations and for annotations on annotations.  Both
    these kinds of annotations employ a reified version of a triple
    representing either the annotated axiom or the annotated annotation.
    The semantic conditions below recovers the triple itself from the
    reified version.

     Table 4.18: Reified Axioms and Annotations

     - if x in ICEXT(IS(owl:Axiom))
          <x,u> in IEXT(IS(owl:subject))
          <x,p> in IEXT(IS(owl:predicate))
          <x,w> in IEXT(IS(owl:object))
       then <u,w> in IEXT(p))
     - if x in ICEXT(IS(owl:Annotation))
          <x,u> in IEXT(IS(owl:subject))
          <x,p> in IEXT(IS(owl:predicate))
          <x,w> in IEXT(IS(owl:object))
       then <u,w> in IEXT(p))

- There needs to be a section on the differences from OWL 1 Full
  semantics, talking about comprehension principles, at least. 

- Why is there a partial comprehension principle for propertychains and
  subpropertyof (in Table 4.11)?  See suggestion for Table 4.11 above.

- Why do AllDifferent, AllDisjointClasses, and AllDisjointProperties
  have partial comprehension principles?  I suggest removing second half
  of Table 4.13 or moving it to Section 6.

- Why are there comprehension principles for negative property
  assertions?  I suggest removing second half of Table 4.17 or moving it
  to Section 6.

- I have not examined Section 6 closely.

I am thinking about the comprehension principles and how to best handle
them.  I may have a proposal for further changes in this area.

Peter F. Patel-Schneider
Bell Labs Research
Received on Wednesday, 3 September 2008 01:12:11 UTC

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