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Subject: Rough notes on decidability/semantic reasoning thoughts I expressedduring the telecon today


Could XDI be decidable?
Looking at it one way XDI can't be decidable without resolving the issue of XRI being usable as both a role and a concept.
This is true, if we say XDI has n-ary predicates where n > 1, predicates that take 2 or more arguments.
For example the $p in $s/$p/$o is a binary predicate, i.e. $p($s,$o)
 
But...
.. Every XDI $ predicate is a form of some kind of $is$a expression or a negation of such an expression
.. Every $is$a negation is a $is$a of the complement of the object
.. Every $is$a statement can be viewed as a monadic predicate for set membership of the object, essentially the
    object is the predicate
.. Every XDI non $ predicate for form $S/$P/$O is a monadic predicate expression of the form $S$P($O)
.. Every one of the monadic predicates above is a test for set membership, which matched XDI model because we've said it is based on set membership
.. Essentially this turns XDI into a monadic predicate calculus
.. As a result I propose we can say XDI is decidable
 
Need a proof from me and Giovanni and I need to get with Giovanni and discuss how difficult this proof would be. There are existing proofs for a monadic predicate calculus being decidable, so we would I think only need to prove that XDI was a monadic predicate calculus and decidability would follow.
 
Why us decidability important/useful? Because it's necessary to do reasoning that's guaranteed to complete without hanging, and complete in a usable time frame.
 
Why is semantic reasoning useful?
http://videolectures.net/eswc08_blanco_sr/
http://www.ibm.com/developerworks/web/library/wa-semweb/
http://encyclopedia.jrank.org/articles/pages/6898/Semantic-Web.html
http://www.semanticoverflow.com/questions/74/what-are-the-benefits-of-the-semantic-web-to-publishers
 
In short:
.. You can mine your data for new knowledge much more efficiently and garner knowledge you couldn't without reasoning
.. You can automate data mediation from one data structure to another (e.g. PDX Person to FOAF Person)
.. You can easily add metadata to your data, or extend your data, without breaking or rewriting existing data processing
.. Your search, visualization, and reporting tools now can present you with the needles of knowledge that you need, rather than haystacks of raw data you need to sift through - saving you time, money, and manpower.
 
"I'll believe it when I see it, who's actually using this semantic stuff now?", I've heard that in many forms many times over the last year, but...
.. Netflix
.. Google
.. Twitter
.. US Government
.. Best Buy
.. and the number is growing (see this for some use cases: http://www.scientificamerican.com/article.cfm?id=semantic-web-in-actio)
 
From the third article above, the ways semantic reasoning can be used:
  • Consistency - determine if the model is consistent. For example, presents an OWL model containing the facts: (a) cows are vegetarian, (b) sheep are animals, and (c) a ‘mad cow’ is one that has eaten sheep brain. From these facts a computational reasoning engine can infer that ‘mad cows’ are inconsistent since any cow eating sheep violates (a). The following (incomplete, but informative) OWL snippets help illustrate some salient issues. Informally, note the description of mad_cow (line 1). Note that mad_cow is an intersection class (line 4) defined as any cow (line 5) that has a property ‘eats’ (line 6) such that the range of that property (i.e. what it eats) is a part_of a sheep (lines 11, 13) and that part is a ‘brain’ (line 16). Below note that the ‘sheep’ class is defined as subclass of ‘animal’ while ‘cow’ is a subclass of ‘vegetarian’.
  • Subsumption – infer knowledge structure, mostly hierarchy; the notion of one artifact being more general than another. For example, presents a model incorporating the notions (a) ‘drivers drive vehicles’, (b) ‘bus drivers drive buses’, and (b) a bus is a vehicle, and subsumption reasoning allows the inference that ‘bus drivers are drivers’ (since ‘vehicle’ is more general than ‘bus’).
  • Equivalence - determine if classes in the model denote the same set of instances
  • Instantiation - determine if an individual is an instance of a given Class. This is also known as ‘classification’ – that is, determine the instance of a given Class.
  • Retrieval - determine the set of individuals that instantiate a given Class
  •  
     


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