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

To: Pat Hayes <phayes@xxxxxxx>
Cc: OpenOntologyRepository-discussion <oor-forum@xxxxxxxxxxxxxxxx>
From: Ali SH <asaegyn+out@xxxxxxxxx>
Date: Wed, 19 Oct 2011 11:20:04 -0400
Message-id: <CADr70E0f6Q5pdfiCsT0kGpddz4go2mhqtnrWAHvi=5_1pPq3RA@xxxxxxxxxxxxxx>
Dear Pat and Bijan,

On Tue, Oct 18, 2011 at 6:52 PM, Pat Hayes <phayes@xxxxxxx> wrote:
Guys, you have to adapt your terminology to the people you are trying to communicate with. In the OWL/RDF/RIF/Semantic-Web/LInked-Data world, there is no such thing as an 'inference rule'.  (If there were, it would be a line of code inside an inference engine; but most inference engines don't work that way in any case, but instead build tableaux. The textbook terminology of formal logic has not been used in the applied ontology world for about the last two decades.)

Thank you for your discussion and clarification, it's been very helpful! 

Allow me to attempt re-phrasing what's been said. In contrast to a paradigm for ontologies like Cyc, whereby one tries to model the domain as faithfully and completely in one formalism and then delegates reasoning tasks based on the analysis of this expressive representation; in this context we have more of a bottom-up, a priori engineered approach? Before you begin your representation, you partition your domain into different types of knowledge and use a variety of representation / rule languages to capture different parts of intuitions. Simplifying greatly, does this fairly capture the essence of the paradigm?

All this said, I'm still a touch flummoxed at being able to adequately and consistently distinguish an axiom from a rule. For example, the standard inheritance / subclass relation of:

(forall (x) (if (dog x) (animal x)))

is supported by virtually all DL's. It seems like it could be a rule to me. I mean, Pellet or Racer would be able to use the class structure in an OWL-DL ontology to tell me that the properties of Animals apply to Dogs.

[PH] So, now, let us switch back to logical terminology, and I will put scare quotes around the earlier usages. Are 'rules' axioms? Yes, pretty much, if we are talking baout the Horn-clause style of rule; although there are 'rule' languages which allow one to say things that cannot be said in normal logics, eg default assumptions, negation-by-failure, closed-world presumptions, etc.. 


[BP] No as true anymore [re inference rules]. "Consequence" based reasoning is becoming more popular esp. in restricted fragments such as EL, e.g.,

Given these two statements, and putting aside the sociological issues for a moment, in this case, one can determine whether something is a "rule" really only in the context of the expressivity of a particular representation language? Roughly, anything that can't be represented in the formalism is considered a rule? I.e. say I want to represent a fragment of law, I can only decide what is a rule by first deciding which formalism and reasoner I'm using, then anything that couldn't be expressed in said language is a candidate for a rule? 

In summary, what one means by a rule is wholly dependent on what representation language one deploys?

Other people I've spoken to suggest that there is fundamentally something distinct about the notion of a rule from what should be contained in an ontology, which seems like a different issue altogether? They suggest that "concepts and rules" should be treated separately. The description provided by Pat seem more to do with engineering, while those in the previous sentences hinge on a particular interpretation of ontology. 


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