Conceptual Graph Rules and Equivalent Rules: A Synthesis

Mugnier, Marie-Laure

doi:10.1007/978-3-642-03079-6_3

Cited by 2 publications

(1 citation statement)

References 9 publications

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“…9z (ỹ,z), where ↵, are conjunctions of atoms over constants and variables. Such rules occur in many scenarios and are widely known under di↵erent names such as tuple-generating dependencies or Datalog with value invention in databases [2,19], Datalog± in ontological knowledge representation (see [14] and references there in), and conceptual graph rules in diagrammatic reasoning [26].…”

Section: Introductionmentioning

confidence: 99%

Expressiveness of guarded existential rule languages

Gottlob

Rudolph

Šimkus

2014

Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

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The so-called existential rules have recently gained attention, mainly due to their adequate expressiveness for ontological query answering. Several decidable fragments of such rules have been introduced, employing restrictions such as various forms of guardedness to ensure decidability. Some of the more well-known languages in this arena are (weakly) guarded and (weakly) frontier-guarded fragments of existential rules. In this paper, we explore their relative and absolute expressiveness. In particular, we provide a new proof that queries expressed via frontier-guarded and guarded rules can be translated into plain Datalog queries. Since the converse translations are impossible, we develop generalizations of frontier-guarded and guarded rules to nearly frontierguarded and nearly guarded rules, respectively, which have exactly the expressive power of Datalog. We further show that weakly frontier-guarded rules can be translated into weakly guarded rules, and thus, weakly frontier-guarded and weakly guarded rules have exactly the same expressive power. Such rules cannot be expressed in Datalog since their query answering problem is ExpTime-complete in data complexity. We strengthen this completeness result by proving that on ordered databases with input negation available, weakly guarded rules capture all queries computable in exponential time. We then show that weakly guarded rules extended with stratified negation are expressive enough to capture all database queries decidable in exponential time, without any assumptions on the input databases. Finally, we note that the translations of this paper are, in general, exponential in size, but lead to worst-case optimal algorithms for query answering with the considered languages.

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Section: Introductionmentioning

confidence: 99%