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Initial ideas on Distributed Reasoning. Expressivity. The subset of RDF/OWL and that has rule-based inference – OWL –RL In general, datalog Example: rdfs:domain , range, subClassof , subPropertyof Inverseof , transitive property, symmetic property, …. RDF/OWL -> Datalog. Subproperty

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expressivity
Expressivity
  • The subset of RDF/OWL and that has rule-based inference – OWL –RL
  • In general, datalog
  • Example:
    • rdfs:domain, range, subClassof, subPropertyof
    • Inverseof, transitive property, symmetic property,
rdf owl datalog
RDF/OWL -> Datalog
  • Subproperty
  • Subclass
  • Class instance
  • Property instance
  • Redirection
  • P(x,y) :- Q(x,y) .
  • C(x) :- D(x) .
  • C(a) .
  • P(a,b) .
  • a=b.
rdf owl datalog1
RDF/OWL -> Datalog
  • Domain
  • Range
  • Transitive P
  • Symmetric P
  • Functional P
  • InverseFunctional P
  • Inverse of
  • C(x) :- P(x,y)
  • C(y) :- P(x,y)
  • P(x,y) :- P(x,z), P(z,y)
  • P(x,y) :- P(y,x)
  • SameAs(x,y) :- P(z,x),P(z,y)
  • SameAs(x,y) :- P(x,z),P(y,z)
  • Q(x,y) :- P(y,x)
rdf owl datalog2
RDF/OWL -> Datalog
  • Conjunction
  • Disjunction
  • Property Chain
  • Negation
  • Has Value
  • Cardinality
  • C(x) :- A(x), B(x) .
  • C(x) :- A(x). C(x):- B(x).
  • R (x,y):- P(x,z), Q(z,y) .
  • C(x):- not D(x) .C(x): - #count{x, P(x,y)}<=0 .
  • C(x) :- P(x,a) .
  • C(x) : #count{x, P(x,y)}>=3 .

This is also query language

remote join free
Remote Join Free
  • Assumption: data are distributed; rule set is relatively small, every node has the full rule set
    • Data can be duplicated in GIDS manner
  • If there is no join, the result set can be a simple union
    • Domain, range, subC, subP, inverseOf, symmetric, disjunction, has value
  • Each node compute a local answer, the whole answer set is their union
mapreduce
MapReduce

Negation and cardinality queries can be distributed by MapReduce (counting)

void map(String name, String document):

// name: document name

// document: document contents

for each word w in document:

EmitIntermediate(w, "1");

void reduce(String word, IteratorpartialCounts):

// word: a word

// partialCounts: a list of aggregated partial counts

int result = 0;

for each pc in partialCounts:

result += ParseInt(pc);

Emit(AsString(result));

Also see: http://ayende.com/Blog/archive/2010/03/14/map-reduce-ndash-a-visual-explanation.aspx

remote join
Remote Join
  • E.g. C(x) :- D(x), E(x)
    • Node 1: { D(a) }
    • Node 2: { E(a) }
  • One solution: in query answering, do dependency check, and copy partial result to one place
  • E.,g. C1(x) : - D(X) C2(x) :-E(X)
    • Copy instances of C1 and C2 to one node
    • On that node, add rule C(x) :-C1(x), C2(x)
  • Optimization: hashing or indexing?
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