Reasoning about Sets via Atomic Decomposition
| Title | Reasoning about Sets via Atomic Decomposition |
| Publication Type | Technical Report |
| Year of Publication | 1996 |
| Authors | Ohlbach, H. Yürgen, & Koehler J. |
| Other Numbers | 1041 |
| Keywords | arithmetic reasoning, concept languages, description logics, number restrictions |
| Abstract | 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. |
| URL | http://www.icsi.berkeley.edu/ftp/global/pub/techreports/1996/tr-96-031.pdf |
| Bibliographic Notes | ICSI Technical Report TR-96-031 |
| Abbreviated Authors | H. J. Ohlbach and J. Koehler |
| ICSI Publication Type | Technical Report |