Ali, (01)
That's a much clearer way of saying what I was trying to say in another
thread. Decidable logic may be a valuable piece of design for a useful
application, while not also being the common semantic framework (for
many self contained contexts the two may be indistinguishable, I
suspect). A common semantic framework is another reason to use ontology
formats, as a business conceptual model, and an old fashioned engineer
like me would expect to see that before the clever blokes come along and
do the whizzy applications. (02)
Mike (03)
Ali Hashemi wrote:
> To add one more perspective to this discussion.
>
> From a very practical standpoint, the proliferation of "guaranteed
> logics" has at least two unintended consequences.
>
> 1) Company A uses decidable logic L1 (say an internally developed
> temporal logic), while Company B uses decidable logic L2 (say OWL-DL).
> Later A and B realize they want to exchange information and/or combine
> systems. The model and proof theory of their logics are somewhat
> idiosyncratic. Without a more encompassing framework (i.e. Common
> Logic?) or a common semantic foundation, the translation between these
> logics (syntax, semantics and all), let alone their axioms is at best
> not trivial.
>
> Perhaps this situation is mitigated if someone somewhere specifies
> mappings from L1 and L2 to some common foundation logic (see
>
>http://www.informatik.uni-bremen.de/agbkb/forschung/formal_methods/CoFI/hets/index_e.htm
>
> ). But note, that for each dialect of a logic (not just the ontology),
> a further mapping is needed. Unless of course we can somehow make sure
> that everyone uses the same specialized logic...
>
> 2) As a corollary to what John describes below, by sacrificing
> expressiveness for decidability, we also further hinder
> interoperability. Particularly, if we only represent the fragment of
> the problem under consideration that is expressible in said language,
> we are leaving a lot of the intended semantics of the problem domain
> external to the system of representation!
>
> Any other person /or machine /coming along can at best only guess at
> what the actual intent of these squiggles are, since so much is
> consequently left unsaid. A lot of the problems that arise when trying
> to conduct semantic / ontology mappings become much more directly
> accessible. One need only look at the current state of the art in
> semantic mapping based on DL's to see the problems posed by this
> approach. We're trying to match lexical terms, guessing at instance
> data and using probabilities to guess at the intended semantics. If
> more were expressed, we could actually use model theory to specify
> much more robust and reliable mappings.
>
> *Note:* one can still decide to infer / implement only particular
> fragments of the representation, but the representation is more
> complete and closer to the intended semantics of the ontologist /
> knowledge engineer.
>
> ==
>
> None of this is meant to take anything away from the work done on OWL
> or DL's, but I submit that the framing or promoting of these languages
> as "more appropriate" ontology languages, because they guarantee
> decidability is missing the mark, and probably counter productive and
> needlessly divisive / creating silos in a community that really can't
> afford to fragment.
>
> Fragments of logic which exhibit certain desirable properties are an
> important / invaluable toolkit in any ontologist / knowledge
> engineer's repertoire. Being able to mark a fragment of an ontology as
> exhibiting XYZ properties and guaranteeing ABC performance is
> important, and can make the difference in certain domains. But it is
> /not/ the same as ontology, and it would be disingenuous to construe
> such languages as being somehow inherently more suited to
> computational ontology.
>
> To my limited mind, they represent /one /of many useful applications.
> If I'm designing an autonomous robot, I'll probably be using a
> dedicated temporal reasoner, a dedicated spatial reasoner, etc. etc.
> OWL-2 is probably too expressive for these, and not nearly expressive
> enough to support narrative. No single optimized logic or formalism on
> its own is likely to suffice, and I'd rather represent as much as I
> can formally, and /then/ worry about how best to compute these
> explicit assumptions - probably (no - in fact, exactly) based on the
> invaluable work that people in the DL community are doing determining
> the properties of various fragments of FOL. But to start with DL's as
> the end all seems sort of like lobotomizing logic...
>
> My two cents.
>
> Best,
> Ali
>
>
> On Thu, Aug 12, 2010 at 2:37 AM, John F. Sowa <sowa@xxxxxxxxxxx
> <mailto:sowa@xxxxxxxxxxx>> wrote:
>
> On 8/11/2010 6:16 PM, Pat Hayes wrote:
> > Or (just to keep the record clear) another option is to simply
> abandon
> > this quest to achieve decidability, and work with semi-decidable
> > complete logics such as classical FOL.
>
> Yes, and some groups, including Cyc and VivoMind, go a bit farther:
>
> 1. Note that the complexity class (including P, NP, or
> undecidable) is
> *not* a property of a logic, but of problems stated in the logic.
>
> 2. If you use a very expressive logic, you are not required to use
> all possible features of that logic in every problem.
>
> 3. Instead, you can use a variety of inference engines optimized
> for different subsets. (In the case of Cyc, they have about
> three dozen different inference engines optimized for various
> subsets of CycL.)
>
> 4. For all the common cases and many rare cases, it is possible
> to perform a quick syntactic check to determine the complexity
> class of the given problem. Then assign the problem to an
> appropriate inference engine (or sometimes different engines
> for different aspects of a complex problem).
>
> 5. For most cases, it is possible to give the user a guarantee
> of performance on a particular problem (if it is an easy one)
> or a warning (if it is a hard one). For those rare cases,
> where the complexity class cannot be determined, it is also
> possible to say that as part of the warning.
>
> > As Ian points out in another message in this thread, this means that
> > one cannot then undertake to offer users a universal *guarantee* of
> > performance
>
> True, but Cyc could also provide a guarantee for most if not all
> the cases for which an OWL reasoner can provide a guarantee. But
> Cyc can also offer to do its best effort on those problems for
> which a guarantee is not possible.
>
> As that article on the issue of P=NP points out, many problems,
> such as graph isomorphism (GI), that may take exponential time
> have a huge number of efficient special cases. For example,
> the *only* cases for which GI takes exponential time are ones
> where the upper bound on the branching factor of the graph is
> O(n) -- i.e., the number of links to any node is proportional
> to the total number n of nodes in the graph.
>
> For conceptual graphs and even RDF graphs, the branching factor
> is almost never O(n). It's usually bounded by a constant or
> at worst by a polynomial in (log n).
>
> > In our case, it would mean that all this plethora of multiple
> > standards and notations (RDFS, OWL, OWL2, RIF, RuleML,
> WhatNextML...)
> > could be simply described as being what they in fact are, which is
> > various subsets of classical FO logic, or of ISO Common Logic. One
> > parser could handle all of them, all expressed in a single notation,
> > and the work of re-designing a syntax and a new semantics, and
> writing
> > a bundle of close-to-unreadable specification documents would
> not have
> > to be re-done every few years.
>
> Certainly. That's what Cyc does. They have been able to handle a
> huge range of options by implementing different inference engines.
> But the users and SMEs don't have to worry about (or even know about)
> the complexity classes or the inference engines. For most cases,
> even the knowledge engineers don't have to worry, except in the
> unusual cases where they have to add another inference engine or
> revise the tests for choosing which inference engine to use.
>
> For many problems, it's also possible to write a static analyzer
> and compiler that extracts axioms from Cyc and translates them
> to an optimized form for inference engines outside of Cyc.
> See, for example, the approach that Bill Andersen and his
> buddies implemented. I discuss that on p. 6 of the following:
>
> http://www.jfsowa.com/pubs/fflogic.pdf
> Fads and fallacies about logic
>
> John
>
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