Approximate Deduction This material by Holger Wache VU
Approximate Deduction This material by Holger Wache (VU, Knowledge Web)
Approximation (in Semantic Web System) q Real World t DL-Reasoning in EXPTIME (OWL DL in NEXPTIME) Ontology Toy Examples Input DLReasoning Output 2
Approximation Approaches q Language Weakening + Input Ontology q Knowledge Compilation q Approximate DL- Reasoning Deduction Output 3
Approximate Deduction through Simplification Reasoner Simplified Query q q q Quality q q Simplify query Simple query fast query answering Simple query approximated answers Incremental completion of the query Anytime behavior t 4
How to simplify? Rewrite some parts (e. g. , ) Qµ Q Cadoli-Schaerf-Approximation Query = … u> u … u ( …t t …) > Qµ Q 5
Cadoli-Schaerf. Approximation for DLs q Depth of subconcept D: number of universal quantifiers that have D in its scope. Depth: 0 Depth: 2 Depth: 1 6
Approximation Approaches q Language Weakening + Input Ontology q Knowledge Compilation q Approximate DL- Reasoning Deduction Output 7
Approximation through Language Weakening T-Box A-Box OWL-FULL OWL-DLP Knowledge Ontology Base DLPReasoning Input Rolefree Data. Base Queries Reasoning DLReasoning Method Output 8
Approximation Approaches q Language Weakening + Input Ontology q Knowledge Compilation q Approximate DL- Reasoning Deduction Output 9
Approximation through Knowledge Compilation Ontology (optimized) Input Reasoning Method (optimized) Output 10
Approximation through Knowledge Compilation 1. Get rid of nominals. [language weakening] 2. Translate into clausal form. 3. Saturate TBox+RBox by taking all consequences. [compilation] 4. Eliminate function symbols. OWL-DL DLReasoning Disjunctive LP Resolutio n q Compile – OWL-DL Disjunctive LP – Complete but incorrect q [approximate deduction] Deduce – regarding disjunctive heads of rules as conjunctions – Use SLD resolution 11
Approximation through Knowledge Compilation 1. Get rid of nominals. [language weakening] 2. Translate into clausal form. 3. Saturate TBox+RBox by taking all consequences. [compilation] 4. Eliminate function symbols. OWL-DL DLReasoning Disjunctive LP Resolutio n q Compile – OWL-DL Disjunctive LP – Complete but incorrect q [approximate deduction] Deduce – regarding disjunctive heads of rules as conjunctions – Use SLD resolution – Complete but incorrect 12
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