# Adding Threshold Concepts to the Description Logic EL

From International Center for Computational Logic

# Adding Threshold Concepts to the Description Logic EL

*Talk by Oliver Fernández Gil*

- Location: APB 3027
- Start: 11. May 2016 at 2:50 pm
- End: 11. May 2016 at 3:50 pm
- Research group: Automata Theory
- Event series: KBS Seminar
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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 use the relaxed instance query approach of Ecke et al. 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.