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Re: [ontolog-forum] [ontology-summit] Proposed RDF FHIR syntax feedback

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Wed, 11 Mar 2015 13:40:02 -0400
Message-id: <55007DF2.7030107@xxxxxxxxxxx>
Leo, John B, Kingsley, and Phil,    (01)

I agree with Leo about the development of description logics,
but I'd like to extend the history both backward and forward:    (02)

  1. Aristotle developed ontology (his 10 categories and subcategories)
     and the first T-box (the syllogisms for reasoning about inheritance
     and constraints on the hierarchy).    (03)

  2. Porphyry (3rd century AD) drew the first surviving tree diagrams
     for representing hierarchies.  (But there are clues in earlier
     manuscripts that diagrams may have been used much earlier --
     for example, the words 'higher' and 'lower' for talking about
     the categories.)    (04)

  3. Aristotle and his successor Theophratus mentioned if-then rules,
     but the Stoic logicians developed them into a significant subset
     of propositional logic.    (05)

They used the term 'categorical syllogism' for the T-Box, 'hypothetical
syllogism' for forward and backward chaining with if-then rules, and
'disjunctive syllogisms' for inclusive and exclusive or.  For more,
see http://www.jfsowa.com/talks/aristo.pdf    (06)

For a recent conference about lattices of concepts, types, or sorts,
see http://ceur-ws.org/Vol-1252/    (07)

> the Wikipedia page discusses ABox and TBox, I'm not convinced that
> the definition is sufficient. It says, "TBox statements describe a
> conceptualization, a set of concepts and properties for these concepts"
> and "Together ABox and TBox statements make up a knowledge base".    (08)

William of Ockham was much clearer and more precise than that.  He also
developed an early version of model theoretic semantics for stating the
truth conditions for the three kinds of syllogisms (expressed in Latin).    (09)

> I still don't know who coined the terms ABox and TBox.    (010)

Leo and Phil cited the original paper that introduced those terms:
http://aaaipress.org/Papers/AAAI/1983/AAAI83-005.pdf    (011)

> Basically, we should be able to collectively curate a glossary of terms,
> without being impeded by the futile pursuit of global consensus.    (012)

There was a global consensus about the Aristotelian subset that lasted
until the end of the 19th century.  But symbolic logic with its
mathematical notation struck fear in the hearts of people who flunked
high-school algebra.    (013)

But it's possible to introduce full first-order logic in just six
slides.  See slides 7 to 12 of http://www.jfsowa.com/talks/clintro.pdf    (014)

I admit that it takes a full one-hour lecture to get people to feel
comfortable with the notation.  But once they do, they have the basis
for defining the terms used in logic, ontology, and related subjects
without presupposing a single word in any natural language.    (015)

John    (016)

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