Reasoning about Sets via Atomic Decomposition

TitleReasoning about Sets via Atomic Decomposition
Publication TypeTechnical Report
Year of Publication1996
AuthorsOhlbach, H. Yürgen, & Koehler J.
Other Numbers1041
Keywordsarithmetic reasoning, concept languages, description logics, number restrictions

We introduce a new technique that translates cardinality information about finite sets into simple arithmetic terms and thereby enables a system to reason about such set cardinalities by solving arithmetic equation problems.The atomic decomposition technique separates a collection of sets into mutually disjoint smallest components ("atoms") such that the cardinality of the sets are just the sum of the cardinalities of their atoms.With this idea it is possible to have languages combining arithmetic formulae with set terms, and to translate the formulae of this combined logic into pure arithmetical formulae.As a particular application we show how this technique yields new inference procedures for concept languages with so called number restriction operators.

Bibliographic Notes

ICSI Technical Report TR-96-031

Abbreviated Authors

H. J. Ohlbach and J. Koehler

ICSI Publication Type

Technical Report