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Title: | First-order definable counting-only queries | Authors: | HELLINGS, Jelle GYSSENS, Marc Van Gucht, Dirk Wu, Yuqing |
Issue Date: | 2019 | Publisher: | SPRINGER | Source: | ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE, 87(1-2), p. 109-136 | Abstract: | Many data sources can be represented easily by collections of sets of objects. For several practical queries on such collections of sets of objects, the answer does not depend on the precise composition of these sets, but only on the number of sets to which each object belongs. This is the case k= 1 for the more general situation where the query answer only depends on the number of sets to which each collection of at most k objects belongs. We call such queries k-counting-only. Here, we focus on k-SyCALC, i.e., k-counting-only queries that are first-order definable. As k-SyCALC is semantically defined, however, it is not surprising that it is already undecidable whether a first-order query is in 1-SyCALC. Therefore, we introduce SimpleCALC-k, a syntactically defined (strict) fragment of k-SyCALC. It turns out that many practical queries in k-SyCALC can already be expressed in SimpleCALC- k. We also define the query language GCount- k, which expresses counting-only queries directly by using generalized counting terms, and show that this language is equivalent to SimpleCALC-k. We prove that the k-counting-only queries form a non-collapsing hierarchy: for every k, there exist (k+ 1)-counting-only queries that are not k-counting-only. This result specializes to both SimpleCALC- k and k-SyCALC. Finally, we establish a strong dichotomy between 1-SyCALC and SimpleCALC- k on the one hand and 2-SyCALC on the other hand by showing that satisfiability, validity, query containment, and query equivalence are decidable for the former two languages, but not for the latter one. | Notes: | [Hellings, Jelle] Univ Calif Davis, Dept Comp Sci, Exploratory Syst Lab, Davis, CA 95616 USA. [Hellings, Jelle; Gyssens, Marc] Hasselt Univ, Fac Sci, Martelarenlaan 42, B-3500 Hasselt, Belgium. [Van Gucht, Dirk] Indiana Univ, Sch Informat Comp & Engn, 919 E 10th St, Bloomington, IN 47408 USA. [Wu, Yuqing] Pomona Coll, 185 E 6th St, Claremont, CA 91711 USA. | Keywords: | Bag of sets; Counting-only query; First-order definable query; Satisfiability;Bag of sets; Counting-only query; First-order definable query; Satisfiability | Document URI: | http://hdl.handle.net/1942/29993 | ISSN: | 1012-2443 | e-ISSN: | 1573-7470 | DOI: | 10.1007/s10472-019-09652-8 | ISI #: | 000491609600005 | Rights: | Springer Nature Switzerland AG 2019 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2020 |
Appears in Collections: | Research publications |
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hellings 1.pdf Restricted Access | Published version | 757.82 kB | Adobe PDF | View/Open Request a copy |
paper-revised2.pdf | Peer-reviewed author version | 443.82 kB | Adobe PDF | View/Open |
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