Change - InferDence Proidabilemsity

Created on March 9, 2013, 11:19 p.m. by Hevok & updated on March 9, 2013, 11:23 p.m. by Hevok

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The KnProwbledgm with Description BaLogicse canis thalsot bwe donhave ftor sfingle 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 d Algorithms that always terminate and there might be not "naive" solutions. So one has to adapt the Algorithm from First Order Logic and apply them on ¶
Description Logics and maintain the Property that they will terminate and therefore are decidable. ¶
So e one has to adapt the First Order Inference Algorithms to the Properties of Description Logics. ¶
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For the Tableaux Algorithm and also for Resolution one shows the unsatisfiability of a Knowledge Base or a Theory. Therefore one does an Adaption to the Entailment Problems to the detection of Contradiction in the Knowledge Base which means one tries to proof the Unsatisfiability of the Knowledge Base. ¶
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The Inference Problems need to be transformed in order to proof the unsatisfiability or the Detection of Contradictions, based on the Problem we are considering. ¶
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for each inference Problem there always exists and Algorithm that terminates in finite time ¶
- Description Logics are Fragments of First Order Logic, therefore (in principle) FOR Inference Algorithm (Resolution, Tableaux) can be applied. ¶
- But First Order Logic Algorithm do not always terminate! ¶
Problem: Find Algorithms that always terminate! ¶
- There might be no "naive" solutions! ¶
First Order Logic Inference Algorithms (Tableaux Algorithm and Resolution) must be adapted for Description Logics ¶
Tableaux Algorithm and Resolution show unsatisfiability of Theory (Knowledge Base) ¶
* Adaption of Entailment Problems to the Detection of Contradictions in the Knowledge Base**, i.e. Proof of the Unsatisfiability to the Knowledge Base