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Disjunctive datalog with existential quantifiers: Semantics, decidability, and complexity issues

Published online by Cambridge University Press:  05 September 2012

MARIO ALVIANO ,
WOLFGANG FABER ,
NICOLA LEONE  and
MARCO MANNA
MARIO ALVIANO
Affiliation:
Department of Mathematics, University of Calabria, Italy (e-mail: alviano@mat.unical.it, faber@mat.unical.it, leone@mat.unical.it, manna@mat.unical.it)
WOLFGANG FABER
Affiliation:
Department of Mathematics, University of Calabria, Italy (e-mail: alviano@mat.unical.it, faber@mat.unical.it, leone@mat.unical.it, manna@mat.unical.it)
NICOLA LEONE
Affiliation:
Department of Mathematics, University of Calabria, Italy (e-mail: alviano@mat.unical.it, faber@mat.unical.it, leone@mat.unical.it, manna@mat.unical.it)
MARCO MANNA
Affiliation:
Department of Mathematics, University of Calabria, Italy (e-mail: alviano@mat.unical.it, faber@mat.unical.it, leone@mat.unical.it, manna@mat.unical.it)
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Abstract

Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic language. Disjunctive Datalog is useful in a wide range of applications, ranging from Databases (e.g., Data Integration) to Artificial Intelligence (e.g., diagnosis and planning under incomplete knowledge). However, in recent years an important shortcoming of Datalog-based languages became evident, e.g. in the context of data-integration (consistent query-answering, ontology-based data access) and Semantic Web applications: The language does not permit any generation of and reasoning with unnamed individuals in an obvious way. In general, it is weak in supporting many cases of existential quantification. To overcome this problem, Datalog∃ has recently been proposed, which extends traditional Datalog by existential quantification in rule heads. In this work, we propose a natural extension of Disjunctive Datalog and Datalog∃, called Datalog∃,˅, which allows both disjunctions and existential quantification in rule heads and is therefore an attractive language for knowledge representation and reasoning, especially in domains where ontology-based reasoning is needed. We formally define syntax and semantics of the language Datalog∃,˅, and provide a notion of instantiation, which we prove to be adequate for Datalog∃,˅. A main issue of Datalog∃ and hence also of Datalog∃,˅ is that decidability is no longer guaranteed for typical reasoning tasks. In order to address this issue, we identify many decidable fragments of the language, which extend, in a natural way, analog classes defined in the non-disjunctive case. Moreover, we carry out an in-depth complexity analysis, deriving interesting results which range from Logarithmic Space to Exponential Time.

Keywords

datalognon-monotonic reasoningdecidabilitycomplexity
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 12 , Issue 4-5: 28th International Conference on Logic Programming , July 2012 , pp. 701 - 718
Copyright
Copyright © Cambridge University Press 2012

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