Re: [ontology-summit] Clarification re Big Data Challenges Synthesis

[Simon Spero <sesuncedu@xxxxxxxxx>]

On Tue, Apr 3, 2012 at 3:14 AM, Mike Personick <mike@xxxxxxxxxx> wrote:

[ses wrote:] I cannot properly interpret "Higher expressivity often involves more than one piece of information from the abox – meaning you have to cross server boundaries. With lower expressivity you can replicate the ontology everywhere on the cluster and answer questions LOCALLY." 

[mp lists a transitive property, P, [1], two assertions involving this property [2] + [3] (P(a,b) and P(b,c), and the entailment [4] (P(a,c) --  I am assuming that the variables in [2] and [3] are meant to be constants - otherwise, as assertions, they alpha reduce to each other. 

 

A match on [1]+[2]+[3] entails [4], but this is impossible to answer locally.  [1] is part of the ontology, which could be replicated to all nodes, but [2] and [3] come from the instance data, which is scattered across the cluster.

Informally, we have two claims here: (prefixing all variables with ?, and 

[5]  There cannot exist a node ?n  that can know that  P(a,c)

[6]  For all ?x,?y, and ?z, there cannot exist a node ?n which knows that P(?x,?y)  and that P(?y,?z) 

Since by assumption, all nodes know [1] , [6]  entails [5] ; we can disprove [5] by showing that the existence of the disputed node is possible.  Constructing counter examples is trivial.  

Suppose a system distributes assertions to nodes in predicate major order, so that assertions are distributed in P-major order. Further, let such a system distribute assertions such that for transitive properties, assertions that P(x,?y) and P(?y,?z) are preferentially assigned to the same node.  Even without indexing, this operation can be performed in polynomial time (e.g. taking closure of symmetric adjacency matrix).

Alternatively, performing blocking by  placing linked objects in nearyby locations (this is how many OODBMS achieved high performance; similar properties can be found in network database systems like IDMS).  

In order to support [5], we must make [6] an axiom, in which case we must also require that the number of nodes equal the number of instances. 

To justify a weaker, probabilistic form of [5] we need a weaker form of [6], which would hold that the probability of related instances being on the same node is low.  This is not a desirable property to enforce. 

Simon

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