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Journal on Data Semantics

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01.03.2013 | Original Article

The Complexity of Lattice-Based Fuzzy Description Logics

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verfasst von: Stefan Borgwardt, Rafael Peñaloza

Erschienen in: Journal on Data Semantics | Ausgabe 1/2013

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Abstract

We study the complexity of reasoning in fuzzy description logics with semantics based on finite residuated lattices. For the logic \(\mathcal SHI \), we show that deciding satisfiability and subsumption of concepts, with or without a TBox, are ExpTime-complete problems. In \(\mathcal{ALCHI }\) and a variant of \(\mathcal{SI }\), these decision problems become PSpace-complete when restricted to acyclic TBoxes. This matches the known complexity bounds for reasoning in crisp description logics between \(\mathcal{ALC }\) and \(\mathcal SHI \).

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In \({L\text{-}\mathcal{SI }_\mathsf c }\), roles are restricted to be crisp.

For special lattices, in particular total orders with the so-called Zadeh semantics, this blowup can be avoided [30].

It is easy to find the remaining \(n-m\) witnesses. For each \(y\in \Delta ^\mathcal I \) we have \(r^\mathcal I (x,y)\,{\otimes } \,C^\mathcal I (y)\le (\exists r.C)^\mathcal I (x)\) and thus, any choice of additional elements of the domain would suffice.

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Titel: The Complexity of Lattice-Based Fuzzy Description Logics
From to
verfasst von: Stefan Borgwardt
Rafael Peñaloza
Publikationsdatum: 01.03.2013
Verlag: Springer-Verlag
Erschienen in: Journal on Data Semantics / Ausgabe 1/2013
Print ISSN: 1861-2032
Elektronische ISSN: 1861-2040
DOI: https://doi.org/10.1007/s13740-012-0013-x

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