Research on information extraction from Web pages (wrapping) has seen much activity recently (particularly systems implementations), but little work has been done on formally studying the expressiveness of the formalisms proposed or on the theoretical foundations of wrapping. In this paper, we first study monadic datalog over trees as a wrapping language. We show that this simple language is equivalent to monadic second order logic (MSO) in its ability to specify wrappers. We believe that MSO has the right expressiveness required for Web information extraction and propose MSO as a yardstick for evaluating and comparing wrappers. Along the way, several other results on the complexity of query evaluation and query containment for monadic datalog over trees are established, and a simple normal form for this language is presented. Using the above results, we subsequently study the kernel fragment Elog$^-$ of the Elog wrapping language used in the Lixto system (a visual wrapper generator). Curiously, Elog$^-$ exactly captures MSO, yet is easier to use. Indeed, programs in this language can be entirely visually specified.
In the article 'Recursive queries on trees and data trees' (ICDT'13), Abiteboul et al., asked whether the containment problem for monadic datalog over unordered unranked labeled trees using the child relation and the descendant relation is decidable. This note gives a positive answer to this question, as well as an overview of the relative expressive power of monadic datalog on various representations of unranked trees.
We study the problem of eliminating recursion from monadic datalog programs on trees with an infinite set of labels. We show that the boundedness problem, i.e., determining whether a datalog program is equivalent to some nonrecursive one is undecidable but the decidability is regained if the descendant relation is disallowed. Under similar restrictions we obtain decidability of the problem of equivalence to a given nonrecursive program. We investigate the connection between these two problems in more detail.
We show that the query containment problem for monadic datalog on finite unranked labeled trees can be solved in 2-fold exponential time when (a) considering unordered trees using the axes child and descendant, and when (b) considering ordered trees using the axes firstchild, nextsibling, child, and descendant. When omitting the descendant-axis, we obtain that in both cases the problem is EXPTIME-complete.
With the ever-increasing volume of data, there is an urgent need to provide expressive and efficient tools to support Big Data analytics. The declarative logical language Datalog has proven very effective at expressing concisely graph, machine learning, and knowledge discovery applications via recursive queries. In this demonstration, we develop Logic Library (LLib), a library of recursive algorithms written in Datalog that can be executed in BigDatalog, a Datalog engine on top of Apache Spark developed by us. LLib encapsulates complex logic-based algorithms into high-level APIs, which simplif…
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 pro…
University of Bamberg（班贝格大学）；Leipzig University（莱比锡大学）；ScaDS.AI Center Dresden/Leipzig（德累斯顿/莱比锡可扩展数据分析与人工智能中心）；LIRMM（法国朗格多克信息、机器人与微电子实验室）；Inria（法国国家信息与自动化研究所）；University of Montpellier（蒙彼利埃大学）；CNRS（法国国家科学研究中心）；University of Warsaw（华沙大学）
Oxford-Man Institute of Quantitative Finance（牛津-曼量化金融研究所）；University of Oxford（牛津大学）；Carleton University（卡尔顿大学）
Datalog+/- is a family of ontology languages that combine good computational properties with high expressive power. Datalog+/- languages are provably able to capture the most relevant Semantic Web languages. In this paper we consider the class of weakly-sticky (WS) Datalog+/- programs, which allow for certain useful forms of joins in rule bodies as well as extending the well-known class of weakly-acyclic TGDs. So far, only non-deterministic algorithms were known for answering queries on WS Datalog+/- programs. We present novel deterministic query answering algorithms under WS Datalog+/-. In pa…
A classical result in descriptive complexity theory states that Datalog expresses exactly the class of polynomially computable queries on ordered databases. In this paper we extend this result to the case of higher-order Datalog. In particular, we demonstrate that on ordered databases, for all $k\geq2$, $k$-order Datalog captures $(k-1)$-EXPTIME. This result suggests that higher-order extensions of Datalog possess superior expressive power and they are worthwhile of further investigation both in theory and in practice. This paper is under consideration for acceptance in TPLP.
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical algorithms in the case of unions of conjunctive queries, but become difficult or even undecidable when queries are allowed to contain negation. Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation. We introduce a fragment of SQL, called GN-SQL, as well as a fragment of Datalog with stratified negation,…
Extending programming languages with stochastic behaviour such as probabilistic choices or random sampling has a long tradition in computer science. A recent development in this direction is a declarative probabilistic programming language, proposed by Barany et al. in 2017, which operates on standard relational databases. In particular, Barany et al. proposed generative Datalog, a probabilistic extension of Datalog that allows sampling from discrete probability distributions. Intuitively, the output of a generative Datalog program P on an input database D is a probability space over the minim…
Università Roma Tre（罗马第三大学）；Bank of Italy（意大利银行）；Università Sapienza（罗马第一大学）；TU Wien（维也纳工业大学）；University of Oxford（牛津大学）
Datalog^E is the extension of Datalog with existential quantification. While its high expressive power, underpinned by a simple syntax and the support for full recursion, renders it particularly suitable for modern applications on knowledge graphs, query answering (QA) over such language is known to be undecidable in general. For this reason, different fragments have emerged, introducing syntactic limitations to Datalog^E that strike a balance between its expressive power and the computational complexity of QA, to achieve decidability. In this short paper, we focus on two promising tractable c…
Warded Datalog+- extends the logic-based language Datalog with existential quantifiers in rule heads. Existential rules are needed for advanced reasoning tasks, e.g., ontological reasoning. The theoretical efficiency guarantees of Warded Datalog+- do not cover extensions crucial for data analytics, such as arithmetic. Moreover, despite the significance of arithmetic for common data analytic scenarios, no decidable fragment of any Datalog+- language extended with arithmetic has been identified. We close this gap by defining a new language that extends Warded Datalog+- with arithmetic and prove …
The study of node selection query languages for (finite) trees has been a major topic in the recent research on query languages for Web documents. On one hand, there has been an extensive study of XPath and its various extensions. On the other hand, query languages based on classical logics, such as first-order logic (FO) or Monadic Second-Order Logic (MSO), have been considered. Results in this area typically relate an XPath-based language to a classical logic. What has yet to emerge is an XPath-related language that is as expressive as MSO, and at the same time enjoys the computational prope…
