We introduce a family of logics extending the lightweight Description Logic EL, that allows us to define concepts in an approximate way. The main idea is to use a graded membership function m, which for each individual and concept yields a number in the interval [0,1] expressing the degree to which the individual belongs to the concept. Threshold concepts C~t for ~ in {<,<=,>,>=} then collect all the individuals that belong to C with degree ~t. We further study this framework in two particular directions. First, we define a specific graded membership function deg and investigate the complexity of reasoning in the resulting Description Logic tEL(deg) w.r.t. both the empty terminology and acyclic TBoxes. Second, we show how to turn concept similarity measures into membership degree functions. It turns out that under certain conditions such functions are well-defined, and therefore induce a wide range of threshold logics. Last, we present preliminary results on the computational complexity landscape of reasoning in such a big family of threshold logics.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-204523 |
| Date | 14 June 2016 |
| Creators | Fernández Gil, Oliver |
| Contributors | Universität Leipzig, Fakultät für Mathematik und Informatik, Prof. Dr.-Ing. Franz Baader, Prof. Dr. Gerhard Brewka, Prof. Dr.-Ing. Franz Baader, Prof. Dr. Gerhard Brewka, Prof. Dr. habil. Frank Wolter |
| Publisher | Universitätsbibliothek Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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