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.) (01)
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.) (02)
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. (03)
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. (04)
I think this is what the sources cited by Ali are referring to. S (05)
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. (06)
> 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)? (07)
In the OWL/RDF world, definitely (a). However, don't call them 'axioms',
please. (08)
Pat Hayes (09)
On Oct 18, 2011, at 3:41 PM, Ali SH wrote: (010)
>
>
> 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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