Scalable ABox Reasoning: Approaches and Issues

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Scalable ABox Reasoning Approaches and Issues

• Zhengxiang Pan
• SWAT presentation
• Dec.1, 2006

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Outline

• ABox reasoning
• Approaches
• Our approach
• Issues

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What is ABox reasoning?

• Consistency check
• Instance check
• Given an ABox A, an individual a and a concept C,
  decide whether A C(a)
• Realization
• Given an individual a and an ABox A, find the
  most specific concepts C (w.r.t.subsumption) such
  that A C(a)

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Approaches Tableaux

• Used by Racer, FaCT and Pellet
• Basically, repeatedly calls the instance checking
  procedure to test whether the individual in
  question is an instance of a certain concept in
  the subsumption hierarchy
• Various optimization techniques
• semantic branching, dependency-directed
  backtracking
• Limited by the size of memory
• Intractable in the worst cases

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Approaches Description Logic Programs

• A subset of both OWL-DL and the Horn fragment of
  First Order Logic
• Expressivity limited by horn logic
• Not support disjunctions
• KAON2
• Reduce a SHIQ(D) knowledge base to a disjunctive
  datalog program
• OWLIM
• BigOWLIM claimed to be highly scalable

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DL-Lite

• A strict subset of OWL-Lite
• No transitive property
• No allValuesFrom
• No unionOf, complementOf
• No subsumption and equivalence relations between
  object properties
• Anything beyond make reasoning intractable
• Aims at taking advantage of the query answering
  power of RDBMS
• Similar table design as DLDB
• Translate query to SQL and evaluate
• Views on the fly

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EL

• A subset of OWL-DL (support restricted form of
  nominal)
• No allValuesFrom restrictions
• No Cardinality restrictions
• No Union and Negation
• No Inverse properties (and thus symmetric
  properties)
• No Functional and inverse-functional properties
• Used by medical ontology SNOMED, the gene
  ontology and large parts of GALEN ontology
• Not clear how ABox reasoning will be performed

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DL2DB

• Present a logically equivalent knowledge base
  whose (sound and complete) inference system
  appears as a Datalog program
• Currently works on SHI
• Rules are not new, but the proof of equivalence
  used epistemic operators
• Query evaluation is bidirectional top-down and
  bottom-up
• Performance has not been compared to DLDB,
  although they extend our LUBM

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Our approach DLDB

• DL reasoner focuses on TBox reasoning
• Use database schemas to achieve essential ABox
  reasoning
• What we support now
• Transitive properties
• Intersection of classes
• SomeValuesFrom

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ABox rules
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Architecture
ABox reasoning
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Compute transitive closure

• insert ignore into derived_p1
• select sub, obj
• union
• select sub, derived_p1.object
• from derived_p1
• where objderived_p1.subject
• union
• select derived_p1.subject, obj
• from derived_p1
• where subderived_p1.object
• union
• select tc1.subject, tc2.object
• from derived_p1 as tc1, derived_p1 as tc2
• where tc1.objectsub and tc2.subjectobj

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Restrictions

• Chair in univ-bench ontology
• Select subject as id, headOf_view.sourece,
  headOf_view.onto as onto
• From headOf_view, department_view
• Where headOf_view.objectdepartment_view.id

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Intersections

• Create A_view as select from A
• Union
• union(
• Select from c1_view where id in
• (select id from c2_view)
• )

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Issues

• Computing on Transitive closure is scalable
• SomeValuesFrom is scalable up to 30
  universities using MySQL
• SameAs requires a lot of iterations
• Given sameAs sets, hard to track which tables
  those individuals appeared in current table
  design