9 research outputs found
Formal Concept Analysis Methods for Description Logics
This work presents mainly two contributions to Description Logics (DLs) research by means of Formal Concept Analysis (FCA) methods: supporting bottom-up construction of DL knowledge bases, and completing DL knowledge bases. Its contribution to FCA research is on the computational complexity of computing generators of closed sets
Unification in the Description Logic EL
The Description Logic EL has recently drawn considerable attention since, on
the one hand, important inference problems such as the subsumption problem are
polynomial. On the other hand, EL is used to define large biomedical
ontologies. Unification in Description Logics has been proposed as a novel
inference service that can, for example, be used to detect redundancies in
ontologies. The main result of this paper is that unification in EL is
decidable. More precisely, EL-unification is NP-complete, and thus has the same
complexity as EL-matching. We also show that, w.r.t. the unification type, EL
is less well-behaved: it is of type zero, which in particular implies that
there are unification problems that have no finite complete set of unifiers.Comment: 31page
Formal Concept Analysis Methods for Description Logics
This work presents mainly two contributions to Description Logics (DLs) research by means of Formal Concept Analysis (FCA) methods: supporting bottom-up construction of DL knowledge bases, and completing DL knowledge bases. Its contribution to FCA research is on the computational complexity of computing generators of closed sets
Formal Concept Analysis Methods for Description Logics
This work presents mainly two contributions to Description Logics (DLs) research by means of Formal Concept Analysis (FCA) methods: supporting bottom-up construction of DL knowledge bases, and completing DL knowledge bases. Its contribution to FCA research is on the computational complexity of computing generators of closed sets
Mining EL Bases with Adaptable Role Depth
In Formal Concept Analysis, a base for a finite structure is a set of
implications that characterizes all valid implications of the structure. This
notion can be adapted to the context of Description Logic, where the base
consists of a set of concept inclusions instead of implications. In this
setting, concept expressions can be arbitrarily large. Thus, it is not clear
whether a finite base exists and, if so, how large concept expressions may need
to be. We first revisit results in the literature for mining EL bases from
finite interpretations. Those mainly focus on finding a finite base or on
fixing the role depth but potentially losing some of the valid concept
inclusions with higher role depth. We then present a new strategy for mining EL
bases which is adaptable in the sense that it can bound the role depth of
concepts depending on the local structure of the interpretation. Our strategy
guarantees to capture all EL concept inclusions holding in the interpretation,
not only the ones up to a fixed role depth.Comment: AAAI 2021 (Main Track