[Person-ontology] D7 - Which languages are better than OWL?

[Gian Piero Zarri]

    Dear Pat,


Pat Hayes wrote:

>>     Dear Philippe,
>>
>>     Apparently, you have some problems in catching my central point, 
>> which is very simple. Independently then from any representational 
>> trick, from RDF to FCG or other, this point is that, in an n-ary 
>> situation
>
>
> What do you mean by a n-ary *situation* ? The situation being 
> described has no intrinsic 'arity' (a point made many years ago by, I 
> believe, Strawson), because one can go on adding qualifiers endlessly 
> (he did it... at midnight... in the kitchen... last week... with a 
> knife... silently... rapidly...). In fact, this has been used as an 
> argument (to me, convincing) for the naturalness of the binary 
> case-based representation over the use of n-ary relations. 



    Once again, to represent in a reasonably complete way a dynamic 
situation like that represented by "Mary has given a book to Bill", you 
must introduce a predicate in the form of GIVE, MOVE or whatever, and 
take into account the fact that "Mary", "book-1" and Bill" - apart from 
being instances of ordinary concepts in a standard ontology - are also 
characterized by given logical relationships with this predicate. To 
define these relations, you must introduce a role (or case, or thematic 
role or whatever) like SUBJECT or AGENT to describe the 'function' of 
Mary with respect to the predicate, a role OBJECT for the book etc. All 
this ends up, for this example, with the definition of three 'binary' 
relationships, because you can interpret the relationship of Mary to 
GIVE as an 'entity' GIVE that has a 'propriety' SUBJECT that has a 
'value' Mary. The problem is that each of the three binary relationships 
represent, separately, only one facet of the global situation. To 
describe this last in a complete way, you must take the three binary 
relationships CONTEMPORANEOUSLY into account - i.e., you need an 'n-ary' 
form of knowledge representation - and all the reasoning that you could 
do subsequently must necessarily involve this global nature. In the CEUR 
paper I mentioned in one of my last mails to Philippe, there are some 
formal considerations on this matter, but I think that the situation is 
sufficiently clear also expounded simply in natural language.

    I don't understand very well your argument about the "endlessly" 
qualifiers. In one of my previous mails (see also below), I have said 
that, from a concrete point of view, the above example is represented in 
NKRL using an instance of an n-ary template of the type 
"Move:TransferMaterialThingToSomeone" where the slots SUBJ, OBJ and 
BENEFICIARY are necessarily filled; the other (MODAL, CONTEXT etc.) can 
be filled or not depending from the original formulation of the event. 
What you are saying appears to me as a sort of reminiscence of some 
discussions among advocates of a "Kimian" or "Davidsonian" (or 
neo-Davidsonian) definition of "event" about the way of determining 
which specific properties or qualifiers can be considered as 
constitutive of such event, but this has nothing to do with respect to 
the "binary vs. n-ary" discussion. 

>
>
>> like that represented by the event "Mary has given a book to Bill", 
>> you are surely entitled to decompose this situation in a series of 
>> binary relationships, saying, e.g., that Mary is the subject of an 
>> action of giving but, in order to "understand" really this elementary 
>> event, you must necessarily merge again the single binary 
>> relationships in a global unit, (an n-ary one), and to work on this 
>> in a global way.
>
>
> This sounds like CSPeirce reprise. The problem I have with claims like 
> this is that they are so vague that they don't mean anything. Words 
> like ""understand"" (with scare quotes) and "global" have no bearing 
> on any precise semantic theory that I know of. They seem to be vaguely 
> philosophical rhetoric. Now, maybe (in your forthcoming book?) you do 
> have a semantic theory which makes them have some more precise 
> content. If so, can you summarize this for us, briefly?



    My book is not about any sort of "semantic theory", but concerns the 
practical tools I have used and the concrete results I have obtained 
dealing in these last years with the "nonfictional narratives" domain - 
a very important one from a practical point of view. Of course, when I 
have get some formal results about particular aspects of this domain - 
see the normalization of the temporal "theory" of NKRL and its 
utilization in the "fine grained" indexing of NKRL knowledge bases - I 
refer to the corresponding papers. But the domain is probably too large 
(or, at least, too complex for me) to try to set up a complete (and, 
mainly, a non-reductive) sort of axiomatization - note, in this context, 
that the "binary vs. n-ary" is only one of the specific problems you can 
encounter in this field.   

>
>
>> If you deal with the elementary binary relationships separately (this 
>> is what the W3C languages allow at the moment), it is difficult you 
>> will ever be able to move beyond the inferences of the "uncle" type 
>> the SWRL's supporters are fond of.
>
>
> One can show quite rigorously that the translation into a binary 
> framework is what one might call entailment-complete: that is, if P is 
> a set of sentences written using n-ary relations and t(P) is the 
> translation of P into the binary relationships and existential 
> quantifiers (the 'case-based' representation familiar for at least 40, 
> and probably more like 140, years) then if P entails Q then t(P) 
> entails t(Q). The reverse is not true, since there are consequences of 
> the translations (such as the existence of the 'tropes' or n-ary facts 
> as objects) which do not follow from the original. 



    This only shows that, even in a the logical implication specific 
context, binary and n-ary are not equivalent. 


>
>
>>     In NKRL, an event like the above is represented as an instance of 
>> a general, n-ary "template" of the type 
>> "Move:TransferMaterialThingToSomeone", which is a specialization of 
>> a  "Move:TransferToSomeone" template. In the two templates (and in 
>> their instances) the semantic predicate is (conventionally) MOVE, and 
>> the slots SUBJ, OBJ and BENEFICIARY are necessarily filled
>
>
> Why do you say this? One can often infer useful things from incomplete 
> information. It is quite frequently the case that temporal information 
> is missing or incomplete, for example.



    "Complete/incomplete" has nothing to do with "binary/n-ary".


>
>
>> ; the other (MODAL, CONTEXT etc.) can be filled or not depending from 
>> the original formulation of the event. In the concrete instances, the 
>> temporal information must obviously be added. All the inferences are 
>> then executed starting from this unitary, n-ary block.
>
>
> Perhaps you are describing a particular system; but what you say here 
> is certainly not true for general inference of the kind supported by 
> OWL or a logical reasoning engine. And it does not apply to whole 
> categories of real applications (I am particularly thinking of the 
> kinds of reasoning used by intelligence agencies). 



    I am actually working on a "defence" application of NKRL. People who 
have commissioned this work are just trying to go a little bit beyond 
what the "normal" intelligence agencies are doing...


>
>
>> Note, moreover, that I have voluntarily chosen a particularly simple 
>> example, avoiding, e.g., to speak of "connectivity phenomena" in the 
>> style of "Mary has given a book to Bill BECAUSE it was Bill's birthday".
>
>
> Seems to me that this kind of thing is actually easier to express in 
> the binary translation, because the 'tropes' (facts, events,...) are 
> there reified into first-class objects which can themselves take part 
> in relationships and have properties. 




    I agree completely with you: in NKRL, all the "binding 
relationships" of the type COORD, GOAL or CAUSE are "binary". However, 
the reified objects they link together (i.e., the formalizations of the 
basic elementary events) are n-ary.


    Season's greetings,


    G.P. Zarri