Query Containment for Highly Expressive Datalog Fragments

The containment problem of Datalog queries is well known to be undecidable. There are, however, several Datalog fragments for which containment is known to be decidable, most notably monadic Datalog and several "regular" query languages on graphs. Monadically Defined Queries (MQs) have been introduced recently as a joint generalization of these query languages. In this paper, we study a wide range of Datalog fragments with decidable query containment and determine exact complexity results for this problem. We generalize MQs to (Frontier-)Guarded Queries (GQs), and show that the containment problem is 3ExpTime-complete in either case, even if we allow arbitrary Datalog in the sub-query. If we focus on graph query languages, i.e., fragments of linear Datalog, then this complexity is reduced to 2ExpSpace. We also consider nested queries, which gain further expressivity by using predicates that are defined by inner queries. We show that nesting leads to an exponentially increasing hierarchy for the complexity of query containment, both in the linear and in the general case. Our results settle open problems for (nested) MQs, and they paint a comprehensive picture of the state of the art in Datalog query containment.Comment: 20 page

Die Innovation und Diffusion des Drei-Liter-Autos

Der Beitrag gibt einen Überblick über Potentiale und Grenzen der Entwicklung und Verbreitung des Drei-Liter-Autos in Deutschland – im Kontext der ökologischen Modernisierung. Dabei kommt den Mechanismen der Umweltinnovation und der Innovationsdiffusion eine spezielle Bedeutung zu. Welche staatlichen Aktivitäten im Automobilbereich haben die Umweltinnovation Drei-Liter-Auto beeinflusst? Und: Kann das Drei-Liter-Auto national bzw. international erfolgreich sein? Von besonderem Interesse ist das Wechselspiel von Politik und Technik in diesem Prozess; aber auch die relevanten Akteure (Politik, Greenpeace, Industrie) sowie deren Strategien, Maßnahmen und Ziele. Zur Innovation des Drei-Liter-Autos in Deutschland hat die Politik vor allem mit marktwirtschaftlichen Instrumenten und einem kalkulierbaren Politikstil beigetragen sowie durch das gebildete Netzwerk mit der Autoindustrie. Gleichwohl fehlen politische Maßnahmen, die Diffusion der Drei-Liter-Pkw entscheidend zu stimulieren. Die Umweltpolitik Deutschlands reicht nicht aus, um internationale Lead-Markt-Effekte zu erzielen – obgleich zahlreiche Potentiale vorhanden sind. Derzeit ist das Segment der Drei-Liter-Fahrzeuge in Deutschland noch ein regionaler Pilotmarkt.The paper, which is to be seen in the context of ecological modernisation, gives an analysis of the potentials and limits of the development and diffusion of fuel efficient automobiles (so called “3-literautomobiles”) in Germany. The mechanisms of environmental innovation and those of their diffusion are of particular importance. In this respect quite a few questions arise. The focus is on the question on what kind of government actions – within the domain of the automobile industry – did influence the environmental innovations. Furthermore it is studied if the 3-liter-car can be expected to be successful on the German and on the international markets. But innovation is a highly difficult task, especially for governments. Of special interest is the interplay between policy and technology, and the actors configuration that have been involved, as well as their strategies, measures and goals. By introducing economic instruments and a calculable policy-style as well as the forming of a network with the automobil industry, the German policy contributed to the innovation of the 3-liter-automobile. Nevertheless, political measures aimed at stimulating the diffusion of the 3-literautomobile are lacking. Even though numerous potentials are available, Germany´s environmental policy is not able to obtain international lead-market effects. At present, the 3-liter-automobile segment is still only a regional pilot market

Description Logic Reasoning with Decision Diagrams: Compiling SHIQ to Disjunctive Datalog

We propose a novel method for reasoning in the description logic SHIQ. After a satisfiability preserving transformation from SHIQ to the description logic ALCIb, the obtained ALCIb Tbox T is converted into an ordered binary decision diagram (OBDD) which represents a canonical model for T. This OBDD is turned into a disjunctive datalog program that can be used for Abox reasoning. The algorithm is worst-case optimal w.r.t. data complexity, and admits easy extensions with DL-safe rules and ground conjunctive queries

Type-elimination-based reasoning for the description logic SHIQbs using decision diagrams and disjunctive datalog

We propose a novel, type-elimination-based method for reasoning in the description logic SHIQbs including DL-safe rules. To this end, we first establish a knowledge compilation method converting the terminological part of an ALCIb knowledge base into an ordered binary decision diagram (OBDD) which represents a canonical model. This OBDD can in turn be transformed into disjunctive Datalog and merged with the assertional part of the knowledge base in order to perform combined reasoning. In order to leverage our technique for full SHIQbs, we provide a stepwise reduction from SHIQbs to ALCIb that preserves satisfiability and entailment of positive and negative ground facts. The proposed technique is shown to be worst case optimal w.r.t. combined and data complexity and easily admits extensions with ground conjunctive queries.Comment: 38 pages, 3 figures, camera ready version of paper accepted for publication in Logical Methods in Computer Scienc

Worst-case Optimal Query Answering for Greedy Sets of Existential Rules and Their Subclasses

The need for an ontological layer on top of data, associated with advanced reasoning mechanisms able to exploit the semantics encoded in ontologies, has been acknowledged both in the database and knowledge representation communities. We focus in this paper on the ontological query answering problem, which consists of querying data while taking ontological knowledge into account. More specifically, we establish complexities of the conjunctive query entailment problem for classes of existential rules (also called tuple-generating dependencies, Datalog+/- rules, or forall-exists-rules. Our contribution is twofold. First, we introduce the class of greedy bounded-treewidth sets (gbts) of rules, which covers guarded rules, and their most well-known generalizations. We provide a generic algorithm for query entailment under gbts, which is worst-case optimal for combined complexity with or without bounded predicate arity, as well as for data complexity and query complexity. Secondly, we classify several gbts classes, whose complexity was unknown, with respect to combined complexity (with both unbounded and bounded predicate arity) and data complexity to obtain a comprehensive picture of the complexity of existential rule fragments that are based on diverse guardedness notions. Upper bounds are provided by showing that the proposed algorithm is optimal for all of them

Datalog-Expressibility for Monadic and Guarded Second-Order Logic

We characterise the sentences in Monadic Second-order Logic (MSO) that are over finite structures equivalent to a Datalog program, in terms of an existential pebble game. We also show that for every class C of finite structures that can be expressed in MSO and is closed under homomorphisms, and for all ?,k ?there exists a canonical Datalog program ? of width (?,k), that is, a Datalog program of width (?,k) which is sound for C (i.e., ? only derives the goal predicate on a finite structure ? if ? ? C) and with the property that ? derives the goal predicate whenever some Datalog program of width (?,k) which is sound for C derives the goal predicate. The same characterisations also hold for Guarded Second-order Logic (GSO), which properly extends MSO. To prove our results, we show that every class C in GSO whose complement is closed under homomorphisms is a finite union of constraint satisfaction problems (CSPs) of ?-categorical structures

Derivation-Graph-Based Characterizations of Decidable Existential Rule Sets

This paper establishes alternative characterizations of very expressive classes of existential rule sets with decidable query entailment. We consider the notable class of greedy bounded-treewidth sets (gbts) and a new, generalized variant, called weakly gbts (wgbts). Revisiting and building on the notion of derivation graphs, we define (weakly) cycle-free derivation graph sets ((w)cdgs) and employ elaborate proof-theoretic arguments to obtain that gbts and cdgs coincide, as do wgbts and wcdgs. These novel characterizations advance our analytic proof-theoretic understanding of existential rules and will likely be instrumental in practice.Comment: accepted to JELIA 202