Reasoning in DL OWL: Reasoning

1
Reasoning in DL OWL Reasoning

• Muhammad Rafi

2
Agenda

• What is Reasoning ?
• DL and Reasoning Rules?
• Problems in Reasoning with DL?
• OWL Reasoning Software's
• Conclusion

3
Reasoning?

• Knowledge all information and an understanding
  to carry out tasks and to infer new information
• Information -- data equipped with meaning
• Data -- un-interpreted signals that reach our
  senses
• Intelligence- play of knowledge

4
Reasoning

• Reasoning is the cognitive process of looking for
  reasons for beliefs, conclusions, actions or
  feelings.
• Reason is a way of thinking characterized by
  logic, analysis, and synthesis.

5
Semantics

• Semantics is ?(KB) by translating KB into FOL
• It is hard to decipher via machine processing
• DL tends to put reasoning process in
  undecidability?
• Computational time for reasoning

6
Goal of DL in Ontology?

• Extending OWL-DL with rules is needed
• query answering should be decidable
• SWRL approach is undecidable
• We wish to know
• explain why adding rules to DL leads to
  undecidability
• present DL-safe rules
• discuss the expressivity of the approach
• show that query answering is decidable
• give an algorithm for query answering

7
Descriptive Logic

• OWL-DL a decidable fragment of FOL
• allows existential and universal quantifiers
• quantifier usage restricted to make reasoning
  decidable
• only tree-like axioms allowed
• expressivity not sufficient for certain practical
  problems
• Rule systems a different set of choices
• decidability achieved by allowing universal
  quantifiers only
• existential quantifiers possible (function
  symbols required easily lead to undecidability)
• usually support non-monotonic reasoning

8
Concept Expression

• Atomic concepts
• C
• C u D
• C ? D
• ? R.C
• R.C
• n R.C (R is simple)
• n R.C (R is simple)
• i1, , in

9
Roles

• Atomic roles
• R (inverse roles)

10
TBox

• C D
• C ? D

11
ABox

• ABox reasoning (reasoning about instance data).
• C(a)
• R(a,b)
• a ? b
• a b

12
RBox

• R S
• Trans(R)

13
Problem of Reasoning
14
Example
15
DL in Ontology

• Knowledge is correct (captures intuitions)
• Does C subsume D w.r.t. ontology O? (in every
  model I of O, CI µ DI )
• Knowledge is minimally redundant (no unintended
  synonyms)
• Is C equivallent to D w.r.t. O? (in every model I
  of O, CI DI )
• Knowledge is meaningful (classes can have
  instances)
• Is C is satisfiable w.r.t. O? (there exists some
  model I of O s.t. CI ? C )
• Querying knowledge
• Is x an instance of C w.r.t. O? (in every model I
  of O, xI lt CI )
• Is hx,yi an instance of R w.r.t. O? (in every
  model I of O, (xI,yI) lt RI )

16
DL in Ontology?

• All reducible to KB satisfiability or concept
  satisfiability w.r.t. a KB
• Can be decided using highly optimised tableaux
  reasoners

17
OWL Reasoners

• Pellet (TBox)
• FaCT(RBoxMonotonic Reasoning)
• Racer Pro (ABox)

18
Questions????