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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