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The chase algorithm is a fundamental tool for query evaluation and query containment under constraints, where the constraints are (sub-classes of) tuple-generating dependencies (TGDs) and equality generating depencies (EGDs). So far, most…
Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…
The celebrated Trakhtenbrot's theorem states that the set of finitely valid sentences of first-order logic is not computably enumerable. In this note we will extend this theorem by proving that the finite satisfiability problem of any…
We prove that adding upwards closed first-order dependency atoms to first-order logic with team semantics does not increase its expressive power (with respect to sentences), and that the same remains true if we also add constancy atoms. As…
Sound exhaustiveness checking of pattern-matching is an essential feature of functional programming languages, and OCaml supports it for GADTs. However this check is incomplete, in that it may fail to detect that a pattern can match no…
Data exchange heavily relies on the notion of incomplete database instances. Several semantics for such instances have been proposed and include open (OWA), closed (CWA), and open-closed (OCWA) world. For all these semantics important…
When specifying security policies for databases, it is often natural to formulate disjunctive dependencies, where a piece of information may depend on at most one of two dependencies P1 or P2, but not both. A formal semantic model of such…
So-called combined approaches answer a conjunctive query over a description logic ontology in three steps: first, they materialise certain consequences of the ontology and the data; second, they evaluate the query over the data; and third,…
Ontology embeddings map classes, relations, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic…
We study a fitting problem inspired by ontology-mediated querying: given a collection of positive and negative examples of the form $(\mathcal{A},q)$ with $\mathcal{A}$ an ABox and $q$ a Boolean query, we seek an ontology $\mathcal{O}$ that…
Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extra…
A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely…
Open Domain Question Answering (ODQA) within natural language processing involves building systems that answer factual questions using large-scale knowledge corpora. Recent advances stem from the confluence of several factors, such as…
The chase procedure is a fundamental algorithmic tool in databases that allows us to reason with constraints, such as existential rules, with a plethora of applications. It takes as input a database and a set of constraints, and iteratively…
We study first-order logic (FO) over the structure consisting of finite words over some alphabet $A$, together with the (non-contiguous) subword ordering. In terms of decidability of quantifier alternation fragments, this logic is…
We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…
In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology. To correctly compute answers to queries, it is necessary to perform complex reasoning over the constraints…
We present sensitivity analysis for results of query executions in a relational model of data extended by ordinal ranks. The underlying model of data results from the ordinary Codd's model of data in which we consider ordinal ranks of…