Change - Inference Problems

Created on March 9, 2013, 11:19 p.m. by Hevok & updated on March 9, 2013, 11:20 p.m. by Hevok

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. ¶
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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. ¶
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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? ¶
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Also one can also ask about Class equivalency, is C equal to D, so are two Classes really the same? ¶
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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. ¶
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It might also be interesting to ask for Class Membership, i.e. is an Individual a contained in class C? ¶
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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. ¶
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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)" ¶
- Find all (known!) Individuals of Class C*