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Re: [oor-forum] Ontologies vs Theories / Axioms vs Rules

To: Christopher Menzel <cmenzel@xxxxxxxx>
Cc: OpenOntologyRepository-discussion <oor-forum@xxxxxxxxxxxxxxxx>
From: Ali SH <asaegyn+out@xxxxxxxxx>
Date: Tue, 18 Oct 2011 16:41:17 -0400
Message-id: <CADr70E2FGbb2fog8N48vqCc2iaQHe9qSsk0uSqH-KEc51p9u6Q@xxxxxxxxxxxxxx>

On Tue, Oct 18, 2011 at 4:16 PM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:
On Oct 18, 2011, at 10:06 PM, Ali SH wrote:
> Dear Leo and Chris,
> Thanks for the responses. I understand the distinction between an inference rule and an axiom,

Right, as I'd suspected (and so noted at the bottom of my post).

Noted, but not acknowledged in my initial email response :D. 

> the issue for me stems from a terminological confusion, because obviously, an axiom can express a rule (not in the same sense as an inference rule; i.e. if X is an employee then Y assigns X an employee number).

Looks like an axiom to me. :-)  "Rule" just seems to have a pragmatic connotation that what is expressed is something that *ought* to be done by whoever is playing a certain role (Y, presumably, in this case).

In the LKIF paper, they have statements such as:  

This is well explained in Deliverable D1.1, where LKIF itself is discussed: for more complex or other types of knowledge than terminological knowledge we also need rule formalisms. (page 3 in [1])

There are also several rule-based approaches that try to capture norms in rules with notions like violation or duty as antecedent or conclusion. The rule itself captures the meaning of the norm, so that the confusion between norm and normative statementis again retained. (page 35 in [1])

Which suggests to me that they aren't referring to inference rules. But I have no clue how to reliably distinguish a rule from an axiom. In  [2] http://www.estrellaproject.org/doc/D1.1-LKIF-Specification.pdf, they have a section describing their rules, which seems to me to be a mix of axioms and inference rules.

For example, these seem like axioms to me (page 74 in [2]):

(rule §-9-306-1

(if (and (goods ?s ?c)
(consideration ?s ?p)
(collateral ?si ?c)
(collateral ?si ?p)
(holds (perfected ?si ?c) ?e)
(unless (applies §-9-306-3-2 (perfected ?si ?p))))
(holds (perfected ?si ?c) ?e)))

(rule §-9-306-2a

(if (and (goods ?t ?c)
(collateral ?s ?c))
(not (terminates ?t (security-interest ?s)))))
(fact F1 (not (terminates T1 (security-interest S1))))
(fact F2 (collateral S1 C1))

> That said, your interpretation of rule poses an interesting question, do people distinguish an ontology from an ontology + whatever inference rules used to interpret it?

Inference rules simply come packaged with whatever logic one is building one's ontology on (or affixing one's ontology axioms to).

That's what I thought.

> Based on analogy then, does gmail as software refer to the gmail the source code, or gmail the compiled, deployed code?

Sorry, man, that's too heavy for me! :-)

I have a feeling this question has been tread before.... ;) 

> When people refer to an ontology (or an ontology artifact), are they referring singularly to (a) the axioms, or (b) the axioms under deductive closure, or (c) the axioms in combination(s) with reasoner(s)?

It seems to me that (a) and (b) are two viable meanings for "ontology".  (c) does not seem feasible to me, except insofar as one identifies a reasoner with the logic it is based on.

This is where I guess the analogy with traditional software breaks down. Gmail compiled and deployed seems to me to be (c). Though for ontologies, the line between (b) and (c) are a bit unclear to me. I don't know how someone (i.e. human) would be able to actually access / generate (b) without some reasoner (their mind?).

[1] Joost Breuker, Rinke Hoekstra, Alexander Boer, Kasper van den Berg, Rossella Rubino, Giovanni Sartor, Monica Palmirani, Adam Wyner, and Trevor Bench-Capon. OWL ontology of basic legal concepts (LKIF-Core). Deliverable 1.4, Estrella, 2007.
[2] Alexander Boer, Marcello Di Bello, Kasper van den Ber, Tom Gordon, Andr´as F¨orh´ecz, R´eka Vas. Specification of the Legal Knowledge Interchange Format. Deliverable 1.1, Estrella, 2007



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