Coupling ontologies with document spanners

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Joining Extractions of Regular Expressions

Regular expressions with capture variables, also known as "regex formulas," extract relations of spans (interval positions) from text. These relations can be further manipulated via Relational Algebra as studied in the context of document spanners, Fagin et al.'s formal framework for information extraction. We investigate the complexity of querying text by Conjunctive Queries (CQs) and Unions of CQs (UCQs) on top of regex formulas. We show that the lower bounds (NP-completeness and W[1]-hardness) from the relational world also hold in our setting; in particular, hardness hits already single-character text! Yet, the upper bounds from the relational world do not carry over. Unlike the relational world, acyclic CQs, and even gamma-acyclic CQs, are hard to compute. The source of hardness is that it may be intractable to instantiate the relation defined by a regex formula, simply because it has an exponential number of tuples. Yet, we are able to establish general upper bounds. In particular, UCQs can be evaluated with polynomial delay, provided that every CQ has a bounded number of atoms (while unions and projection can be arbitrary). Furthermore, UCQ evaluation is solvable with FPT (Fixed-Parameter Tractable) delay when the parameter is the size of the UCQ

Joining extractions of regular expressions

Regular expressions with capture variables, also known as “regex formulas,” extract relations of spans (interval positions) from text. These relations can be further manipulated via the relational Algebra as studied in the context of “document spanners,” Fagin et al.’s formal framework for information extraction. We investigate the complexity of querying text by Conjunctive Queries (CQs) and Unions of CQs (UCQs) on top of regex formulas. Such queries have been investigated in prior work on document spanners, but little is known about the (combined) complexity of their evaluation. We show that the lower bounds (NP-completeness and W[1]-hardness) from the relational world also hold in our setting; in particular, hardness hits already single-character text. Yet, the upper bounds from the relational world do not carry over. Unlike the relational world, acyclic CQs, and even gamma-acyclic CQs, are hard to compute. The source of hardness is that it may be intractable to instantiate the relation defined by a regex formula, simply because it has an exponential number of tuples. Yet, we are able to establish general upper bounds. In particular, UCQs can be evaluated with polynomial delay, provided that every CQ has a bounded number of atoms (while unions and projection can be arbitrary). Furthermore, UCQ evaluation is solvable with FPT (Fixed-Parameter Tractable) delay when the parameter is the size of the UCQ

Querying and Repairing Inconsistent Prioritized Knowledge Bases: Complexity Analysis and Links with Abstract Argumentation

In this paper, we explore the issue of inconsistency handling over prioritized knowledge bases (KBs), which consist of an ontology, a set of facts, and a priority relation between conflicting facts. In the database setting, a closely related scenario has been studied and led to the definition of three different notions of optimal repairs (global, Pareto, and completion) of a prioritized inconsistent database. After transferring the notions of globally-, Pareto- and completion-optimal repairs to our setting, we study the data complexity of the core reasoning tasks: query entailment under inconsistency-tolerant semantics based upon optimal repairs, existence of a unique optimal repair, and enumeration of all optimal repairs. Our results provide a nearly complete picture of the data complexity of these tasks for ontologies formulated in common DL-Lite dialects. The second contribution of our work is to clarify the relationship between optimal repairs and different notions of extensions for (set-based) argumentation frameworks. Among our results, we show that Pareto-optimal repairs correspond precisely to stable extensions (and often also to preferred extensions), and we propose a novel semantics for prioritized KBs which is inspired by grounded extensions and enjoys favourable computational properties. Our study also yields some results of independent interest concerning preference-based argumentation frameworks.Comment: 27 pages. To appear in the 17th International Conference on Principles of Knowledge Representation and Reasoning (KR 2020) without the appendi

Document spanners: from expressive power to decision problems

We examine document spanners, a formal framework for information extraction that was introduced by Fagin, Kimelfeld, Reiss, and Vansummeren (PODS 2013, JACM 2015). A document spanner is a function that maps an input string to a relation over spans (intervals of positions of the string). We focus on document spanners that are defined by regex formulas, which are basically regular expressions that map matched subexpressions to corresponding spans, and on core spanners, which extend the former by standard algebraic operators and string equality selection. First, we compare the expressive power of core spanners to three models {namely, patterns, word equations, and a rich and natural subclass of extended regular expressions (regular expressions with a repetition operator). These results are then used to analyze the complexity of query evaluation and various aspects of static analysis of core spanners. Finally, we examine the relative succinctness of different kinds of representations of core spanners and relate this to the simplification of core spanners that are extended with difference operators

Declarative cleaning of inconsistencies in information extraction

The population of a predefined relational schema from textual content, commonly known as Information Extraction (IE), is a pervasive task in contemporary computational challenges associated with Big Data. Since the textual content varies widely in nature and structure (from machine logs to informal natural language), it is notoriously difficult to write IE programs that unambiguously extract the sought information. For example, during extraction, an IE program could annotate a substring as both an address and a person name. When this happens, the extracted information is said to be inconsistent, and some way of removing inconsistencies is crucial to compute the final output. Industrial-strength IE systems like GATE and IBM SystemT therefore provide a built-in collection of cleaning operations to remove inconsistencies from extracted relations. These operations, however, are collected in an ad hoc fashion through use cases. Ideally, we would like to allow IE developers to declare their own policies. But existing cleaning operations are defined in an algorithmic way, and hence it is not clear how to extend the built-in operations without requiring low-level coding of internal or external functions. We embark on the establishment of a framework for declarative cleaning of inconsistencies in IE through principles of database theory. Specifically, building upon the formalism of document spanners for IE, we adopt the concept of prioritized repairs, which has been recently proposed as an extension of the traditional database repairs to incorporate priorities among conflicting facts. We show that our framework captures the popular cleaning policies, as well as the POSIX semantics for extraction through regular expressions. We explore the problem of determining whether a cleaning declaration is unambiguous (i.e. always results in a single repair) and whether it increases the expressive power of the extraction language. We give both positive and negative results, some of which are general and some of which apply to policies used in practice.SCOPUS: ar.jinfo:eu-repo/semantics/publishe