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XDI dictionary, reasoner...
Hello Drummond, All, as for last week's request, I'm reintroducing this issue. After receiving your answer, I tried to figure out how to prove that two XDI RDF statements =giovanni+home+phone/$type$xsd$string/ =giovanni/+home+phone/ does identify the same node. In order to recall the whole issue, which is now also on the wiki thanks to Drummond, http://wiki.oasis-open.org/xdi/XdiReasoners I report hereafter the whole message, at the end my elaborations: ********** Drummond replies ********** I am so glad someone finally asked this question in black and white – I have been thinking about this issue of “XDI expressivity” for months now given the fundamental capabilities of XDI RDF. Forgive me for providing an extended answer, but I think the question can be so revealing about the power of XDI RDF. First, to answer your question right up front, “Do those three XDI addresses identify the same literal node?”, my answer is: “You cannot know deterministically without reference to the XDI dictionaries used by the statements.” The reason is that the three statements represent three different paths through the XDI RDF graph, and as you pointed out, each path represents different semantics. So you you really have to drill all the way down into the graphs, and the statements represented by each graph, in order to answer your question. To do this, let’s start by looking at the three graphs visually in X3 Simple (one reason I love X3 Simple is that it lets you see the visual pattern of the graph while at the same time seeing the addresses). #1 =giovanni+phone+home $type$xsd$string "+39 06 4451843" #2 =giovanni +phone+home "+39 06 4451843" #3 =giovanni+phone +home "+39 06 4451843" Now, let’s “fully explode” each of these into ALL the XDI statements they represent. #1 (5 statements) =giovanni $has +phone =giovanni+phone $has +home $type $has $xsd $type$xsd $has $string =giovanni+phone+home $type$xsd$string "+39 06 4451843" #2 (3 statements) =giovanni $has +phone+home +phone $has +home =giovanni +phone+home "+39 06 4451843" #3 (2 statements) =giovanni $has +phone =giovanni+phone +home "+39 06 4451843" Isn’t it fascinating that the first graph represents five statements, the second three, and the final one only two? In any case, all three options here (plus more - see below) appear to be completely valid chains of XDI statements between the XDI subject =giovanni and the XDI literal "+39 06 4451843". But none of them asserts exactly the same semantics (the only way to do that would be to use XDI synonyms, i.e., $is statements). However using an XDI reasoner and an XDI dictionary (which itself is just a set of XDI statements comprising definitions), you could verify that according to that dictionary, all these statements identify the same literal node. In fact the dictionary is pretty short. Here it is: +phone $is$a <--1--> + $type$xsd$string $has <--2--> +home $a$has <--3--> +home $has$a <--4--> +home $a$has$a <--5--> +home +home $is$a <--6--> + $has <--7--> +phone $a$has <--8--> +phone $has$a <--9--> +phone $a$has$a <--10--> +phone $type $has $xsd $type$xsd $has $string As short as it is, the semantics represented by those statements – while crystal clear from a pure XDI semantics point-of-view – represent a surprising range of grammatical relationships a human POV. Roughly translated to English, the first ten statements say: 1) A phone is both a subject (noun) and a label for a type of data (typically called a “phone number”, but often abbreviated in English as just “phone”). 2) A phone can have a home, i.e., as a noun, it can have a possessive relationship with another noun, home. 3) A phone is something a home can have (possessive relationship). 4) A phone has an attribute of home. 5) Phone is an attribute of a home. 6) Home is a subject. 7) A home can have a phone (possessive relationship – inverse of #3). 8) A home is something a phone can have (possessive relationship – inverse of #2). 9) A home has an attribute of phone (inverse of #5). 10) Home is an attribute of a phone (inverse of #4). Armed with that dictionary, an XDI reasoner can quickly prove that all the following XDI statements identify the same literal: =giovanni+phone+home/$type$xsd$string/ =giovanni+home+phone/$type$xsd$string/ =giovanni/+home+phone/ =giovanni/+phone+home/ =giovanni+phone/+home/ =giovanni+home/+phone/ However, if you remove any of those XDI dictionary statements, some of the above are no longer provably true. For example, if you remove the statements: +phone $has $home +home $a$has +phone Then you could no longer prove that the following two statements identify the same XDI object as the rest: =giovanni+phone+home/$type$xsd$string/ =giovanni/+phone+home/ They MIGHT identify the same literal as the rest, but now you have nothing you can prove that with. There’s much more I’d like to say about this simple dictionary, but I’m out of time. However I encourage everyone who is interested to study it closely. To test your knowledge, here’s a quiz question: “Given the dictionary above, how can you prove that it is valid for the XDI object of all six statements to be a literal string?” =Drummond Now, I think the most important part to understand is related to the semantics underlying the dictionary sentences: +phone $has <--2--> +home $has$a <--4--> +home which in English means 2) A phone can have a home, i.e., as a noun, it can have a possessive relationship with another noun, home. 4) A phone has an attribute of home. $has, according to XDI RDF model v9, is aggregation, meaning that Any two XDI subjects with a $has relationship can be concatenated into a single XRI representing this relationship. Thus +phone+home is the way how aggregation is expressed. Whereas $has$a is defined as a composition. The object in the RDF statement is therefore an "attribute" belonging to the subject. Example similar to the one in XDI RDF v9: =giovanni/$has$a/+hair+color; thus =giovanni/+hair+color/+black should be a valid XDI RDF statement, expressing composition. Quoting from wikipedia, difference between aggregation and composition: Aggregation differs from ordinary composition in that it does not imply ownership. In composition, when the owning object is destroyed, so are the contained objects. In aggregation, this is not necessarily true. For example, a university owns various departments (e.g., chemistry), and each department has a number of professors. If the university closes, the departments will no longer exist, but the professors in those departments will continue to exist. Therefore, a University can be seen as a composition of departments, whereas departments have an aggregation of professors. In addition, a Professor could work in more than one department, but a department could not be part of more than one university. Now, I tried to work out a formal proof using the assertions 1)-10) but I failed in proving that all the following XDI statements identify the same literal: ... =giovanni+home+phone/$type$xsd$string/ =giovanni/+home+phone/ ... Probably I'm missing something (probably some underlying semantics), however, can you give some hints? Maybe we can work out the prove once for all and report this in the wiki/deliverable, as reference? Thanks, Giovanni At 01.32 24/04/2008, Drummond Reed wrote: 4) TECH TOPIC: XDI DICTIONARY AND XDI REASONER On last week's call Giovanni requested that our tech topic this week be the XDI dictionary and XDI reasoner discussion we started on the list. Wikipedia has a good article on semantic reasoners: http://en.wikipedia.org/wiki/Semantic_Reasoner Drummond created a wiki page to capture the email thread for further discussion: http://wiki.oasis-open.org/xdi/XdiReasoners
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