Chris, (01)
Thanks for adding those clarifications: (02)
> RDF(S) and OWL (esp the latter) both have highly structured semantic
> theories that include a number of primitive semantic categories not
> present in CL (e.g., lists and classes). What *is* the case, is that
> the languages for RDF(S) and OWL can be understood to be CL dialects and
> conditions can be placed on the interpretations of those dialects to
> such that the interpretations satisfying those conditions will be (in a
> certain sense) isomorphic to the interpretations specified by the RDF(S)
> and OWL semantics. Both can therefore be represented, in a precise
> sense, in CL. (03)
I'd also like to clarify Chris's point: (04)
1. Common logic and the three dialects defined in the ISO standard
(CLIF, CGIF, and XCL) have been designed to have as little
ontological commitment as possible. (05)
2. But for most applications, more ontology is necessary, and many
logic-based languages, such as RDF(S), OWL, SQL, Prolog, and
others have some built-in structures. As Chris mentioned,
lists and classes are examples. Other languages add sets,
arithmetic, etc. Even KIF (which can be considered the
predecessor of CLIF) had more ontology in it than CL has. (06)
3. One of the design decisions made for CL was to minimize the
ontological commitment in order to allow different applications
add different ontologies for different purposes. One example of
a useful ontology is the _Mathematical Toolkit_ that is defined
for the Z Specification Language (which is also an ISO standard).
It contains sets, bags, numbers, and sequences (which can be used
as lists). (07)
4. To use CL as an upward-compatible extension of a logic-based
language, the basic ontology of that language must be added as
a collection of CL axioms. To use CL as an upward-compatible
extension of a family of languages, the axioms for all of the
ontologies in those languages must be added to CL. (08)
5. Fortunately, the Mathematical Toolkit of Z is sufficiently rich
that it is already a superset of most common ontologies for
such languages. Therefore, adding the axioms of the Z Toolkit
to CL would provide a suitable ontology for them (perhaps with
only a few extra additions, which can be specified in CL). (09)
6. By the way, the axioms for the Z Toolkit are stated in Z, but
fortunately, Z can be translated to CL. Therefore, the Z axioms
for the Toolkit can be translated to CL axioms in any of the
three standard dialects. (010)
7. By a similar method, many other logic-based languages can be
translated to CL. For example, many people use UML diagrams
for specifying systems. Those diagrams are logic-like and
they can be translated to CL, but with some additional
axioms to specify the ontology. The UML activity diagrams,
for example, would require axioms for time-dependencies
between events. Those axioms could also be stated in CL. (011)
This discussion illustrates the rationale for Common Logic: it
provides a common target language for a wide range of different
logic-based languages. RDF(S) and OWL cannot be translated to
Z, and Z cannot be translated to RDF(S) and OWL. But all three
of those languages, plus others such as UML, can be translated
to CL. (012)
John (013)
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