Spectra of Cardinality Queries over Description Logic Knowledge Bases
Quentin Mani\`ere, Marcin Przyby{\l}ko

TL;DR
This paper investigates the spectra of counting queries over Description Logic knowledge bases, identifying their possible shapes and providing effective representations, especially for atomic queries in $ ext{ALCIF}$ and its sublogics.
Contribution
It characterizes the spectra of atomic counting queries over $ ext{ALCIF}$ ontologies and introduces effective representations for these spectra, advancing finite model reasoning techniques.
Findings
Spectra are subsets of natural numbers closed under addition for $ ext{ALCIF}$.
Simpler spectra shapes like $[m, ext{infinity}]$ occur in sublogics.
Computing the spectra representations is $ ext{FP}^{ ext{NP}[ ext{log}]}$-complete.
Abstract
Recent works have explored the use of counting queries coupled with Description Logic ontologies. The answer to such a query in a model of a knowledge base is either an integer or , and its spectrum is the set of its answers over all models. While it is unclear how to compute and manipulate such a set in general, we identify a class of counting queries whose spectra can be effectively represented. Focusing on atomic counting queries, we pinpoint the possible shapes of a spectrum over ontologies: they are essentially the subsets of closed under addition. For most sublogics of , we show that possible spectra enjoy simpler shapes, being or variations thereof. To obtain our results, we refine constructions used for finite model reasoning and notably rely on a cycle-reversion technique for the Horn…
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Taxonomy
TopicsSemantic Web and Ontologies · Advanced Database Systems and Queries · Data Management and Algorithms
MethodsBalanced Selection · Sparse Evolutionary Training
