John F. Sowa wrote: (01)
>
>
> The recent exchange of notes between Michael Gruninger and
> me illustrates the kinds of things that are likely to create
> inconsistencies. Michael wants the Process Specification
> Language (PSL) and the associated reasoning method of situation
> calculus to be included in the core, (02)
I have never, ever, made that claim! (03)
I've been holding my tongue until now, but you cross the line
when you impute invalid positions to me personally. (04)
I have never made any claims about the content of any "core".
My only recommendation (actually more of a plea) is that
any ontology module should be expressed as a fixed set of axioms
written in Common Logic, along with the corresponding model theory. (05)
My objection is with the idea that we should not be mixing
different logical languages with different model theories within the
library.
This simply compounds the problem of determining the relationship
between different modules. (06)
For example, here are some possible relationships:
- consistency of two modules
- entailment of one module by another
- one module is a consistent extension of another module (07)
All of these problems require that the modules use the same logic
with the same model theory. (08)
> but I maintain that it
> should not be in the core because it is inconsistent with the
> more general pi calculus (and related special cases, which
> include Petri nets and UML activity diagrams). (09)
How do we know that it is inconsisent if you do not tell us what
the Common Logic axioms are? (010)
Pi calculus is not an ontology -- it is a language with its own model theory
and proof theory. (011)
As I said before, simply invoking the magic spell "... it can be
translated into FOL"
does not make something an ontology.
Suppose for the sake of argument that a Petri net is specified by a set of
sentences in some formal language L. This set of sentences is not an
ontology.
Any ontology will axiomatize the intended semantics of the nonlogical
lexicon of the sentences which is reusable/sharable across all Petri nets.
What is this nonlogical lexicon? Where is its axiomatization?
The existence of a mapping from L to FOL does not create this
axiomatization. (012)
If pi calculus is an ontology, what is the nonlogical lexicon?
What classes of structures formalize the intended semantics of the
terminology within this lexicon? Are these structures axiomatizable within
Common Logic? (013)
Once you have provided us with the set of Common Logic axioms for pi
calculus,
we can proceed in an objective manner and discuss the relationship to
other modules. (014)
- michael (015)
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