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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…
Ontology-mediated querying and querying in the presence of constraints are two key database problems where tuple-generating dependencies (TGDs) play a central role. In ontology-mediated querying, TGDs can formalize the ontology and thus…
We study the problem of fitting ontologies and constraints to positive and negative examples that take the form of a finite relational structure. As ontology and constraint languages, we consider the description logics $\mathcal{E\mkern-2mu…
When data schemata are enriched with expressive constraints that aim at representing the domain of interest, in order to answer queries one needs to consider the logical theory consisting of both the data and the constraints. Query…
We study the complexity of enumerating the answers of Conjunctive Queries (CQs) in the presence of Functional Dependencies (FDs). Our focus is on the ability to list output tuples with a constant delay in between, following a linear-time…
In this tutorial, we will survey known results on the complexity of conjunctive query evaluation in different settings, ranging from Boolean queries over counting to more complex models like enumeration and direct access. A particular focus…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
Evaluating the reasoning capabilities of Large Language Models is increasingly challenging as models improve. Human curation of hard questions is highly expensive, especially in recent benchmarks using PhD-level domain knowledge to…
In this paper we introduce a new class of tuple-generating dependencies (TGDs) called triangularly-guarded (TG) TGDs. We show that conjunctive query answering under this new class of TGDs is decidable since this new class of TGDs also…
In this paper we introduce a new class of tuple-generating dependencies (TGDs) called triangularly-guarded TGDs, which are TGDs with certain restrictions on the atomic derivation track embedded in the underlying rule set. We show that…
We introduce a temporal model for reasoning on disjunctive metric constraints on intervals and time points in temporal contexts. This temporal model is composed of a labeled temporal algebra and its reasoning algorithms. The labeled…
We study the problem to decide, given sets T1,T2 of tuple-generating dependencies (TGDs), also called existential rules, whether T2 is a conservative extension of T1. We consider two natural notions of conservative extension, one pertaining…
In ontology-based data access (OBDA), the classical database is enhanced with an ontology in the form of logical assertions generating new intensional knowledge. A powerful form of such logical assertions is the tuple-generating…
Even though query evaluation is a fundamental task in databases, known classifications of conjunctive queries by their fine-grained complexity only apply to queries without self-joins. We study how self-joins affect enumeration complexity,…
We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
Solving problems through tool use under explicit constraints constitutes a highly challenging yet unavoidable scenario for large language models (LLMs), requiring capabilities such as function calling, instruction following, and…
In temporal logics, a central question is about the choice of modalities and their relative expressive power, in comparison to the complexity of decision problems such as satisfiability. In this tutorial, we will illustrate the study of…
Text-based games present a unique class of sequential decision making problem in which agents interact with a partially observable, simulated environment via actions and observations conveyed through natural language. Such observations…
We study the enumeration of answers to ontology-mediated queries (OMQs) where the ontology is a set of guarded TGDs or formulated in the description logic ELI and the query is a conjunctive query (CQ). In addition to the traditional notion…