A Logical Formulation of PRMs

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A Logical Formulation of PRMs
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Example

• Institute(InstId,Type)
• Researcher(RID,Area,Salary,InstID)
• Paper(PaperId,Topic)
• Author(RId,PaperID)
• Cites(PaperId1,PaperId2)

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Types of Uncertainty

• intra-relational dependency
• a researchers salary depends on their research
  area
• inter-relational dependency
• a researchers salary depends on the type of
  institute they work at
• reference uncertainty
• a papers author is more likely to be a research
  in the same area as the paper
• exists uncertainty
• a citation between two papers is more likely to
  exist if they are on the same topic
• identity uncertainty
• the authors of two distinct papers are more
  likely to be the same individual if the author
  names are similar and if the co-authors are the
  same

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Keys
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DependsOn Predicates

• Examples
• DependsOn1(Salary Area) ? Researcher(RId,Salary,A
  rea,InstId)
• DependsOn1(Salary Area, Type) ?
  Researcher(RId,Salary,Area,InstId),
  Institute(InstId,Type)

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Rules for DependsOn

• The set of DependsOn predicates occur only in the
  heads of clauses
• The body of a DependsOn clause may contain
  extensional predicates, built-in predicates
• Every descriptive attribute A must appear as the
  first argument of a DependsOn predicate
• If there is more than one DependsOn predicate for
  a particular attribute, require for each
  corresponding key, only one DependsOn matches.

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Aggregates

• A researchers salary depends on the number of
  publications they have
• CountRIDAuthorPaperId(RId,CntPapers)
• this takes the Author relation,
  Author(RId,PaperId) groups by RId and takes the
  count
• Equivalent to
• select RId,count(PaperId) as CntPapers from
  Author group by RId
• More general form
• AggrkeypredicateAggr-Variable-List(Key,AggrVal)

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Syntax

• Predicates ordinary predicates, aggregates,
  DependsOn
• Clauses Key Constraints, DependsOn Clauses
• CPDs

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Semantics

• Attribute Uncertainty
• Background theory provides instantiations for
  both the primary key and foreign keys through a
  set of partially instantiated extensional
  predicates

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A Sample KB

• Researcher-Inst(101)
• Researcher-Inst(102)
• Researcher-Institute-Inst(101,201)
• Researcher-Institute-Inst(102,201)
• Institute-Inst(201)

• Paper-Inst(301)
• Author-Inst(101,301)
• Author-Inst(102,301)
• Paper-Inst(302)
• Author-Inst(101,302)
• Cites-Inst(301-302)

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Intensional Predicates to Introduce RVs

• ?Area, Salary Researcher(RId,Area,Salary,InstId)
  ? Researcher-Institute-Inst(RId,InstId)
• ?Type Institute(InstId,Type) ?
  Institute-Inst(InstId)

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Dependency Graph

• Convert each numbered DependsOn statement to a
  general binary relation ?
• DependsOn(Ai.,A,,) ?
• Let Vi and V, be instantiations
• we add Vi lt V,
• We require lt to be acyclic

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Reference Uncertainty

• Paper(PaperId,Topic), Venue(VenueId,Area),
  PublishedIn(PaperId,VenueID)
• Paper-Inst(301), Paper-Inst(302),
  Venue-Inst(stoc), Venue-Inst(focs),
  Venue-Inst(icse), Venue-Inst(pldi),
  Venue-Inst(isca)
• ? Venue PublishedIn(301,Venue)
• ? Venue PublishedIn(302,Venue)
• VenueKeys VenueId ? VenueId
  Venue-Inst(VenueId)
• VenueKeys stoc,focs,icse,pldi,isca

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FKDependsOn

• FKDependsOn(VenueIdAreaTopic) ?
  PublishedIn(PaperId,VenueId), Paper(PaperId,Topi
  c),Venue(VenueId,Area)
• General form
• FKDependsOn(variableltpartition-variable-listgtltpa
  rentsgt)
• Once a partition is chosen for a variable, the
  key is chosen uniformly from that partition.

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Ensuring Coherence

• We require that the parents and the variables
  that define the partition come before the fk
  variable in the dependency graph
• Also, any dependencies based on the fk must occur
  after the fk is determined.

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Existence Uncertainty

• CiteExists(PaperId1,PaperId2,Exists)
• Cites(PaperId1,PaperId2) ? CiteExists(PaperId1,Pap
  erId2,True)
• DependsOn(ExistsTopic1,Topic2) ?
  CiteExists(PaperId1,PaperId2,Exists),
  Paper(PaperId1,Topic1), Paper(PaperId2,Topic2)

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