Change - DInferencidae Probilityems

Created on March 9, 2013, 11:19 p.m. by Hevok & updated on March 9, 2013, 11:25 p.m. by Hevok

The Inference ofand KEnowtailedgment viafor Description Logic is can problem of Decidabipplity. ¶
All thed Ion speciferenice problems must behat solvned in wa finites time,o ansower withey must bhe dhecidable. ¶
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Whate cand onbe dones nfot know ifr they terminate. ¶
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Thire PrKnobwlemdge withBase Descriptioan Lalsogics is that wbe havdone tfor fsind 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 Basegle 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