- From: Pat Hayes <phayes@ihmc.us>
- Date: Sun, 28 Feb 2016 00:46:03 -0600
- To: Reto Gmür <reto@wymiwyg.com>
- Cc: "Peter F. Patel-Schneider" <pfpschneider@gmail.com>, semantic-web@w3.org
On Feb 26, 2016, at 10:14 AM, Reto Gmür <reto@wymiwyg.com> wrote: > On Fri, Feb 26, 2016, at 14:28, Peter F. Patel-Schneider wrote: >> On 02/26/2016 01:52 AM, Reto Gmür wrote: >>> >>> On Thu, Feb 25, 2016, at 06:18, Pat Hayes wrote: >>>> >>>> On Feb 23, 2016, at 10:24 AM, Reto Gmür <reto@wymiwyg.com> wrote: >>>> >>>>> On Tue, Feb 23, 2016, at 17:05, Peter F. Patel-Schneider wrote: >>>>>> On 02/23/2016 07:31 AM, Reto Gmür wrote: >>>>>>> [...] >>>>>>> >>>>>>> Granted, the semantics of :rangeIncludes are very weak (under OWA) but >>>>>>> the fact that you can create contradictions with it shows that it's not >>>>>>> completely meaningless. >>>>>>> >>>>>>> ex:prop1 s:rangeIncludes :Cat . >>>>>>> :Cat owl:disjointWith :Dog . >>>>>>> ex:prop1 owl:range :Dog . >>>>>>> >>>>>>> The above graph evaluates to false in every possible world, this is not >>>>>>> the case if you omit any of the 3 triples, this shows that >>>>>>> `s:rangeIncludes` is not a meaningless decoration. >>>>>>> >>>>>>> Reto >>>>>> >>>>>> I don't think that this follows from the semantics of :rangeIncludes, >>>>>> even if >>>>>> you augment schema.org semantics with disjointness. >>>>> >>>>> In the example I also used "owl:range" to create what I thought is a >>>>> contradiction. >>>>>> >>>>>> Perhaps one could also count the documentation of >>>>>> rangeIncludes as authoritative as well. So from >>>>>> https://schema.org/rangeIncludes, rangeIncludes "[r]elates a property to >>>>>> a >>>>>> class that constitutes (one of) the expected type(s) for values of the >>>>>> property" would also be part of the semantics of schema.org ranges. >>>>> >>>>> I considered only this definition. And based on that I still think there >>>>> is a contradiction, if the owl:range of a property excludes :Cat (which >>>>> is expressed with the statements using owl-properties), :Cat cannot at >>>>> the same time "be (one of) the expected type(s) for values of the >>>>> property". >>>> >>>> Of course it can. It only follows that the values of this particular >>>> property are all in some other part of the range. According to the >>>> schema.org definition of rangeIncludes, this is quite permissible. >>> >>> I'm not getting you. >>> >>> from >>> >>> (1) :Cat owl:disjointWith :Dog . >>> (2) ex:prop1 rdfs:range :Dog . >>> >>> It follows that: (3) "no value of the property ex:prop1 can be an of >>> type :Cat". >>> >>> Do we agree till here? >>> >>> (4) ex:prop1 s:rangeIncludes :Cat >>> >>> means: (5) "The class :Cat is an expected type for values of the >>> property ex:prop1" >>> >>> Do you agree that (5) follows from (4) when using the definition from >>> http://schema.org/rangeIncludes? >> >> No. This sentence reads as if each expected type for a property is the >> type >> of all values of the property. This is not the case at all in >> schema.org. >> >> Even the slightly weaker statement at https://schema.org/rangeIncludes is >> not >> suitable. The wording there "Relates a property to a class that >> constitutes >> (one of) the expected type(s) for values of the property." also reads as >> if >> each expected type is supposed to be a type of all values of the >> property. >> >>> Agreeing to both (4) and (5) boils down to: >>> >>> - :cat is an impossible type for values of the property ex:prop1 >>> - :cat is an expected type for values of the property ex:prop1 >> >> Not exactly. "Impossible" is a very strong word here, even stronger than >> contradictory. It is certainly possible for a value of a property to >> have a >> type that contradicts the range of the property. It just triggers a >> contradiction (or maybe even something with even less import), which does >> what >> contradictions (or whatever) do in the setup one is currently working in. > > Doesn't "p rdfs:range t" mean that it is *necessary* for all objects of > p to be of type t? No, it simply means that this is a valid inference, ie that p rdfs:range t and x p y together entail y rdf:type t. None of these Web logics (RDFS, OWL, etc.) are modal logics. > If so by modal logic it is *impossible* for an object > of p not to be of type t. > > In how far do you see impossible as stronger than contradictory? If I > ask why something is impossible I'm happy with an answer that proofs > that it would contradict itself or one of the axioms. What more do you > need for impossibility? > > >> >>> Using the first definition of "Expect" from the oxford dictionary as >>> "Regard (something) as likely to happen", I think there is a >>> contradiction between asserting that something is impossible and that >>> something is expected. >> >> Certainly there would be something odd going on in an extended schema.org >> setup if one of the rangeIncludes of a property were disjoint from a true >> range of the property. I do not, however, believe that this oddness is >> anything near a strong contradiction (i.e., something that causes all >> information to be meaningless). > > I think that for any charitable interpretation of > https://schema.org/rangeIncludes for "p schema:rangeIncludes t" to hold > it must be *possible* for an object of p to be of type t. What does this 'possible' mean, exactly? Should we infer that there *must* be some value of p which is in t? (Call this the strict interpretation) Or might it be that, while membership in t is 'possible', that in fact there are no values of p in t? Put another way, is is possible that there are no values of p in t, even though membership in t is possible? (Call this the weak interpretation.) Formally, this depends on which modal logic of necessity and possibility you accept as correct: there are, as I expect you know, more such logics than you can shake a stick at. But the difference is important. > > Of course being "likely" means more than being "possible" but the former > implies the latter and possibility is all that is needed to create a > contradiction with statements of necessity and negation. Suppose we know that (A) p schema:rangeIncludes t1 and that (B) p schema:rangeIncludes t2 Your reasoning, using the strict interpretation, would allow us to conclude that there must be a value of p in t1 and one in t2. But this is incompatible with the disjunctive interpretation of schema:range. So let us instead adopt the weak interpretation. Now assume that one of t1 and t2, say t1, is provably empty, so it is impossible for anything to be of that type. This is consistent with values of p having the property (t1 OR t2), so it is not a contradiction. Even if we only know A, and that t1 is provaby empty, the most we can conclude from the schema definitions is that there must be some other, as yet perhaps unknown, type which is also an expectedvalue of p, ie that p schema:rangeIncludes _:x . and again, there is no contradiction here. Pat Hayes > > > Reto >> >>> >>> I would really like to learn where you think my reasoning is wrong. >>> >>> Cheers, >>> Reto >>> >>>> If you disagree, please suggest how to express the schema semantics as a >>>> precise model-theoretic condition in such a way that it produces the >>>> contradiction you expect. >>>> >>>> Pat Hayes >>>> >>>>> >>>>> Reto >> >> peter >> > > ------------------------------------------------------------ IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32502 (850)291 0667 mobile (preferred) phayes@ihmc.us http://www.ihmc.us/users/phayes
Received on Sunday, 28 February 2016 06:46:33 UTC