Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Bisimulations for Description Logics   We study bisimulations for useful description logics. The simplest among the
considered logics is $\mathcal{ALC}_{reg}$ (a variant of PDL). The others
extend that logic with inverse roles, nominals, quantified number restrictions,
the universal role, and/or the concept constructor for expressing the local
reflexivity of a role. They also allow role axioms. We give results about
invariance of concepts, TBoxes and ABoxes, preservation of RBoxes and knowledge
bases, and the Hennessy-Milner property w.r.t. bisimulations in the considered
description logics. Using the invariance results we compare the expressiveness
of the considered description logics w.r.t. concepts, TBoxes and ABoxes. Our
results about separating the expressiveness of description logics are naturally
extended to the case when instead of $\mathcal{ALC}_{reg}$ we have any sublogic
of $\mathcal{ALC}_{reg}$ that extends $\mathcal{ALC}$. We also provide results
on the largest auto-bisimulations and quotient interpretations w.r.t. such
equivalence relations. Such results are useful for minimizing interpretations
and concept learning in description logics. To deal with minimizing
interpretations for the case when the considered logic allows quantified number
restrictions and/or the constructor for the local reflexivity of a role, we
introduce a new notion called QS-interpretation, which is needed for obtaining
expected results. By adapting Hopcroft's automaton minimization algorithm and
the Paige-Tarjan algorithm, we give efficient algorithms for computing the
partition corresponding to the largest auto-bisimulation of a finite
interpretation.

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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn