Chris, (01)
I just wanted to address one point: (02)
CP> Traditionally logic studies inference and ontology existence. (03)
Whenever anyone uses the word 'traditionally' with regard to logic
and ontology, that immediately triggers a historical response. (04)
Aristotle founded both traditions -- ontology and formal logic.
His method of defining the categories by genus and differentiae
automatically produces a hierarchy (partial ordering). Porphyry
started the tradition of drawing the hierarchy as a tree, and
Leibniz extended the tree to a complete lattice. (05)
But from the very beginning, Aristotle used formal logic (i.e.,
syllogisms) to reason about the hierarchy. In fact, Aristotle's
syllogisms are often called 'categorial syllogisms' to distinguish
them from conditional reasoning by if-then rules, which were
developed in detail by later Greek and medieval Latin logicians.
(And in fact, Aristotle's subset of logic is still the most widely
used core of the description logics, such as OWL. Many ontologies
expressed in OWL use *only* the Aristotelian subset.) (06)
The first major challenge to Aristotle's upper level (his ten
top categories) was by Kant, who proposed 12 categories. But
Kant reinforced the connection between logic and ontology by
using Aristotle's logic as a basis for deriving his categories. (07)
The relationship between logic and ontology has been very clear
from the beginning. Aristotle's first six books, which present
his logic, are called the _organon_ (tool or instrument) because
the logic they present is intended as a tool for doing philosophy
in general, of which ontology is called the *first philosophy*. (08)
For a very brief summary of Aristotle and Porphyry in relation
to the more modern work, see (09)
http://www.jfsowa.com/ontology/ontoshar.htm
Building, Sharing, and Merging Ontologies (010)
In short, logic is a tool for doing ontology. (011)
John (012)
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