Complexity and Expressive Power of Disjunction and Negation in Limit Datalog release_2r7uhzrdaje23ol4bv7x3lrbd4

by Mark Kaminski, Bernardo Cuenca Grau, Egor V. Kostylev, Ian Horrocks

Published in PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE by Association for the Advancement of Artificial Intelligence (AAAI).

2020   Volume 34, Issue 03, p2862-2869

Abstract

Limit Datalog is a fragment of Datalogℤ—the extension of Datalog with arithmetic functions over the integers—which has been proposed as a declarative language suitable for capturing data analysis tasks. In limit Datalog programs, all intensional predicates with a numeric argument are limit predicates that keep maximal (or minimal) bounds on numeric values. Furthermore, to ensure decidability of reasoning, limit Datalog imposes a linearity condition restricting the use of multiplication in rules. In this paper, we study the complexity and expressive power of limit Datalog programs extended with disjunction in the heads of rules and non-monotonic negation under the stable model semantics. We show that allowing for unrestricted use of negation leads to undecidability of reasoning. Decidability can be restored by stratifying the use of negation over predicates carrying numeric values. We show that the resulting language is Π2EXP -complete in combined complexity and that it captures Π2P over ordered structures in the sense of descriptive complexity.We also provide a study of several fragments of this language: we show that the complexity and expressive power of the full language are already reached for disjunction-free programs; furthermore, we show that semi-positive disjunctive programs are coNEXPcomplete and that they capture coNP.
In application/xml+jats format

Archived Files and Locations

application/pdf  538.1 kB
file_76te4a643fbolhbokl6utv4xgq
mx.aaai.org (web)
web.archive.org (webarchive)
application/pdf  285.4 kB
file_skm66xlohbb5vcajfkwhcltj4q
ora.ox.ac.uk (web)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article-journal
Stage   published
Date   2020-04-03
Proceedings Metadata
Not in DOAJ
Not in Keepers Registry
ISSN-L:  2159-5399
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: a4fd86e2-b0bc-4fc1-9d25-979bc5577090
API URL: JSON