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

To: OpenOntologyRepository-discussion <oor-forum@xxxxxxxxxxxxxxxx>
From: Kathryn B Laskey <klaskey@xxxxxxx>
Date: Tue, 18 Oct 2011 21:11:08 -0400
Message-id: <4DF5253A-E6F9-4E3A-BFBB-610255EF9690@xxxxxxx>
Well said. Thanks -- i was planning to write something similar but am too 
swamped to get to it.      (01)

On Oct 18, 2011, at 6:52 PM, Pat Hayes wrote:    (02)

> 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.) 
> 
> That is not what the people that Ali is citing are talking about. In the 
>applied-semantic-web world, traditional logics are not widely used, in fact 
>hardly at all. The most widely used formalisms are description logics; so 
>widely used in fact that for many people, DL's simply *are* the 'language' for 
>writing ontologies, and the very idea of an ontology written any anything 
>other than a DL (except maybe something even less expressive, such as RDF) is 
>not even contemplated or mentioned. However, this world does recognize another 
>class of notations, loosely derived from Prolog or from production systems 
>(which were developed entirely separately from logics and so share almost no 
>scholarly or terminological links with the logic field), which operate by 
>chaining together 'rules' (basically, and oversimplifying, Horn clauses 
>thought of as encoding forward-constrained implications). So there is a large 
>and active field which develops, studies and categorizes "rule languages" 
>which range in complexity from simple Horn-clause forward-inference engines to 
>elaborate things with defaults, exceptions and so on. There is also a usage of 
>"rule" as in 'business rule', and an active area of formalization and 
>standardization for these 'rules' , in which they are seen as essentially 
>deontic rules, encoding normative ways to behave rather than facts which are 
>true or false. And these are still considered to be 'rules' and 'rule 
>languages'. So it is not obvious that it all reduces to Horn clauses in every 
>case. (Merging an assertional with a deontic language would be an interesting 
>challenge.) And then there are logic-programming systems like Prolog, and 
>production systems. All of these have a great deal in common at the 
>implementation level, so they have come to be seen as parts of a single field 
>of 'rule languages', one which now holds its own conferences, journals, 
>standardization committees, etc.. etc..(For example, try googling RuleML.)
> 
> Both of these formalisms -  description logics and rule languages - can be 
>viewed as subcases of FOL (as indeed can relational DBases) and this point of 
>view often seems obvious or trivial to logicians, but it is far from obvious 
>in practice, especially as these fields have developed rather different ways 
>to be practically useful. DL restricts the logical expressivity to a 
>decideable subset of FOL with the finite model property, and its paradigmatic 
>tableaux reasoners achieve completeness within this decidable sub case. (There 
>is a big theoretical literature recording the history and logical 
>ramifications of all this, with links to modal logics and a great deal of 
>advanced model theory.) The rule language tradition is far less logically 
>based and more pragmatic: it typically pays no attention at all to 
>completeness ( OK, I know there are exceptions, but they are achieved only by 
>warping the semantics) and often thinks of the rule languages as more like 
>programming languages than logics. 
> 
> Still, there has been widespread interest in extending the expressive power 
>of a DL logic by adding some of the functionality of a rule language to it. 
>This has the great appeal of keeping the DL fragment intact while allowing 
>inference engines to step outside the DL world where needed, without 
>sacrificing the guarantees of decideability provided by the use of the DL 
>fragment to do the basic consistency chacking which supports practical 
>ontology entailment. Such hybrids have been being proposed, implemented and 
>used since the beginning of the semantic web effort. 
> 
> I think this is what the sources cited by Ali are referring to. S
> 
> 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..  
>However, that terminology of 'axiom' would be anathematic in the ontology 
>world. It smacks of mathematics (which ontology engineering most definitely is 
>not) and it carries the presumption of being an 'assumed truth', which again 
>is inappropriate in this other world. It would be much better to say, 
>statement or expression or sentence, rather than axiom. But yes, many 'rules' 
>are sentences, in fact sentences of the form ((A and B and C) imply D), where 
>A--D are atomic sentences. 
> 
>> 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)?
> 
> In the OWL/RDF world, definitely (a). However, don't call them 'axioms', 
>please. 
> 
> Pat Hayes
> 
> 
> 
> 
> On Oct 18, 2011, at 3:41 PM, Ali SH wrote:
> 
>> 
>> 
>> 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
>> 
>> Best,
>> Ali
>> 
>> 
>> -- 
>> 
>> 
>> (•`'·.¸(`'·.¸(•)¸.·'´)¸.·'´•) .,., 
>> 
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