Inference Problems

Created on March 9, 2013, 11:19 p.m. by Hevok & updated by Hevok on May 2, 2013, 5:35 p.m.

Inference and Entailment for Description Logics can be applied on specific problems that one wants to answer with the help of a given Knowledge Base. In general the Problems of Inference are the following. First of all one is interested whether a Knowledge Base as a whole is consistent or not he other hand if is possible that one can entail the bottom element from a Knowledge base, the it is not consistent.

What can be done for the entire Knowledge Base can also be done for single Class. One can ask whether a Class definition is consistent or must be Class be empty, because the definition is wrong.

On the other hand one can also ask whether a Class inclusion, a Subsumption, i.e. C is part of D. Does is hold or does it not hold?

Also one can also ask about Class equivalency, is C equal to D, so are two Classes really the same?

If one compares two Classes it is also possible that these two Classes disjunctive which means that no Individual is at the same time in Class C and in Class D. One can ask for this, whether two Class are Conjunctive.

It might also be interesting to ask for Class Membership, i.e. is an Individual a contained in class C?

Another thing which one might ask is Instance generation which is a retrieval Problem, i.e. find all x with the Condition C of x which means find all x that are within the Class C.

  • Global (In)Consistency of the Knowledge Base
    • Does the Knowledge Base make sense? KB ⊨ ⊥?
  • Class(in)consistency
    • Must Class C be empty? C ≡ ⊥?
  • Class Inclusion (Subsumption)
    • Structuring the knowledge Base
  • Class Equivalency
    • Are two Classes the same?
  • Class Disjointness
    • Are two Classes disjunctive?
  • Class Membership C(a)?
    • Is individual a contained in Class C?
  • Instance Generation (Retrieval) "find all x with C(x)"

Tags: problems, logic, inferring
Categories: Concept
Parent: Logic

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