Sean, (01)
To see the commonality among various positions, it is helpful
to map them to a common terminology. (02)
> Alternatively, one could treat the taxonomy not as a model,
> (these terms 'are an image of' reality) but as a system of
> differentia (these criteria map reality into this set of terms).
> The question is then not whether one system was more truthlike
> than another, but whether the differentia are adequate for our
> purposes. (03)
In predicate calculus, for example, each differentia is represented
by a monadic predicate, such as isAnimate(x) or isPhysical(x). (04)
The taxonomy is a lattice formed by conjunctions of differentiae.
For any set of differentiae, d1, d2, ..., dN, a new type in the
taxonomy is defined by their conjunction: (05)
t(x) = d1(x) & d2(x) & ... & dN(x). (06)
This is basically the approach used for Aristotle's syllogisms,
which are essentially a subset of OWL. It is also used in FCA
(Formal Concept Analysis) to define a lattice of concepts in
terms of a set of differentiae. (07)
The taxonomy is definitely *not* a model in Tarski's sense
because it only defines monadic predicates or types. It does
not say anything about which types are true or false of anything.
It is also a very limited logic because it does not support
relations with 2 or more arguments. (08)
A Tarski-style model for such a system could be defined by
specifying some set D of individuals, and for each individual
x in D saying which differentiae are true or false of X. (09)
Then Tarski's definitions would determine how the truth of
any first-order statement defined in terms of the base
differentiae could be evalated to T or F. (010)
John Sowa (011)
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