Related papers: Optimally Rewriting Formulas and Database Queries:…
Ontological queries are evaluated against a knowledge base consisting of an extensional database and an ontology (i.e., a set of logical assertions and constraints which derive new intensional knowledge from the extensional database),…
Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…
We consider the evaluation of first-order queries over classes of databases that have bounded degree and low degree. More precisely, given a query and a database, we want to efficiently test whether there is a solution, count how many…
We investigate the following problem: given a sample of classified strings, find a first-order sentence of minimal quantifier rank that is consistent with the sample. We represent strings as successor string structures, that is, finite…
We consider the evaluation of first-order queries over classes of databases with bounded expansion. The notion of bounded expansion is fairly broad and generalizes bounded degree, bounded treewidth and exclusion of at least one minor. It…
Data reconstruction attacks on trained neural networks aim to recover the data on which the network has been trained and pose a significant threat to privacy, especially if the training dataset contains sensitive information. Here, we…
In this work, we introduce the notion of decisional width of a finite relational structure and the notion of decisional width of a regular class of finite structures. Our main result states that given a first-order formula {\psi} over a…
In this paper, we introduce the problem of rewriting finite formal languages using syntactic macros such that the rewriting is minimal in size. We present polynomial-time algorithms to solve variants of this problem and show their…
We study problems connected to first-order logic in graphs of bounded twin-width. Inspired by the approach of Bonnet et al. [FOCS 2020], we introduce a robust methodology of local types and describe their behavior in contraction sequences…
We propose a generic framework for establishing the decidability of a wide range of logical entailment problems (briefly called querying), based on the existence of countermodels that are structurally simple, gauged by certain types of…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
Undecidability of various properties of first order term rewriting systems is well-known. An undecidable property can be classified by the complexity of the formula defining it. This gives rise to a hierarchy of distinct levels of…
This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…
We address the issue of Ontology-Based Data Access, with ontologies represented in the framework of existential rules, also known as Datalog+/-. A well-known approach involves rewriting the query using ontological knowledge. We focus here…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
The Feferman-Vaught theorem provides a way of evaluating a first order sentence $\varphi$ on a disjoint union of structures by producing a decomposition of $\varphi$ into sentences which can be evaluated on the individual structures and the…
Classical algorithms for query optimization presuppose the absence of inconsistencies or uncertainties in the database and exploit only valid semantic knowledge provided, e.g., by integrity constraints. Data inconsistency or uncertainty,…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…
Ontological queries are evaluated against an ontology rather than directly on a database. The evaluation and optimization of such queries is an intriguing new problem for database research. In this paper we discuss two important aspects of…
We introduce tree-width for first order formulae \phi, fotw(\phi). We show that computing fotw is fixed-parameter tractable with parameter fotw. Moreover, we show that on classes of formulae of bounded fotw, model checking is fixed…