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Re: [ontac-forum] Semantics (1, 2, and 3), Ontology and Semiotics

To: Chris Menzel <cmenzel@xxxxxxxx>, ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 31 May 2006 19:05:17 -0400
Message-id: <447E212D.3060003@xxxxxxxxxxx>
Chris,    (01)

Although I'm sure that we agree on how people use ordinary
language, I have been trying to emphasize that there is a
continuum between the informal and the formal.    (02)

CM> Well, as far as actual ontology construction goes, by my
 > lights model theory is actually *prior* in the sense that
 > it should have been worked out as part of the KR system
 > one is using.    (03)

Yes, but all that does it to demonstrate the the KR system
is consistent.  That's good to know, but it doesn't ensure
that what people say so consistently has any relationship
to what they intended to say.    (04)

CM>  An actual ontologist will then use the KR language
 > directly and generally having nothing whatever to do with
 > its model theory in practice, any more than an engineer
 > will have anything to do with the mathematical underpinnings
 > of her calculator.    (05)

This gets into the question of how and whether the mental
models or the engineering models are related to the Tarski-
style models.    (06)

At the end of this note is an excerpt from Section 1.5 of
my 1984 book, _Conceptual Structures_, in which I cite a
comment by Carl Adam Petri (of Petri-net fame).    (07)

Petri claimed that it should be possible to relate
the various kinds of models, and I agreed with him.
Tarski-style models are abstractions from the informal
models, and the primary task of the ontologist or
knowledge engineer is to carry out a systematic analysis
of the informal models in order to develop a representation
that could be directly mapped to a Tarski-style model.    (08)

Note that in the following discussion, I talked about CGs
as models -- the point is that I use ground-level graphs
as a Tarski-style model and the quantified graphs as a
logical notation, whose denotation is determined by a
graph-to-graph mapping to the model.    (09)

____________________________________________________________    (010)

Using language to express a mental model    (011)

The word _model_ has multiple meanings in engineering, logic, and common 
speech. Petri (1977) noted three different meanings in the phrases model 
of an airplane, model of an axiom system, and model farm:    (012)

     * Simulation. A model airplane is a simplified system that 
simulates some significant characteristics of some other system in the 
real world or a possible world.    (013)

     * Realization. A model for a set of axioms is a data structure for 
which those axioms are true. Consistent axioms may have many different 
models, but inconsistent axioms have no model.    (014)

     * Prototype. A model farm is an ideal or standard for evaluating 
other less perfect farms or for designing new ones.    (015)

Petri maintained that a common basis should be found for these three 
different ways of modeling. Conceptual graphs, indeed, form models in 
all three senses of the term: the graphs simulate significant structures 
and events in a possible world; a set of axioms, called laws of the 
world, must at all times be true of the graphs; and certain graphs, 
called schemata and prototypes, serve as patterns or frames that are 
joined to form the models.    (016)

Besides serving as realizations for axioms, mental models must be 
related to the real world if people are to act effectively in it. In 
Fig. 1.5, a policeman is communicating his model of the world to another 
man by means of language. Yet the relationship between language and the 
world is indirect: a sentence must be interpreted in terms of a 
conceptual model, and rules of perception must relate that model to a 
situation. Errors may arise either in mapping language to the model (as 
in the cartoon) or in mapping the model to the world.    (017)

Whether a sentence is true or false depends on the criteria for 
interpreting the sentence in terms of a model and for applying the model 
to the real world. The sentence _This steak weighs 12 ounces_ may be 
true in terms of a model where the standard of weight is a butcher 
scale, but it is probably false in terms of a precision balance.    (018)

To meet the objections to standard logic, conceptual graphs have been 
designed as a more natural notation for logic. They form the semantic 
basis of natural language and represent models of the real world or 
other possible worlds.    (019)

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