TL;DR
This paper explores the computational complexity of ALC subsumption fragments based on Boolean operators and quantifier combinations, revealing a nuanced classification depending on available logical features.
Contribution
It provides a detailed complexity classification of ALC subsumption fragments using Post's lattice and quantifier analysis, extending understanding of description logic complexity.
Findings
Complexity varies with Boolean operators and quantifier combinations.
Classification results form either tripartite or quartering categories.
The approach uses clones in Post's lattice to analyze logical fragments.
Abstract
The subsumption problem with respect to terminologies in the description logic ALC is EXPTIME-complete. We investigate the computational complexity of fragments of this problem by means of allowed Boolean operators. Hereto we make use of the notion of clones in the context of Post's lattice. Furthermore we consider all four possible quantifier combinations for each fragment parameterized by a clone. We will see that depending on what quantifiers are available the classification will be either tripartite or a quartering.
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Taxonomy
TopicsChemical Synthesis and Analysis · semigroups and automata theory · Biomedical Text Mining and Ontologies