Related papers: Characterizing the Program Expressive Power of Exi…
Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep…
Existential rules, also known as data dependencies in Databases, have been recently rediscovered as a promising family of languages for Ontology-based Query Answering. In this paper, we prove that disjunctive embedded dependencies exactly…
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…
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…
Existential rules form an expressive Datalog-based language to specify ontological knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the…
We investigate a family of rule-based logics. The focus is on very expressive languages. We provide a range of characterization results for the expressive powers of the logics and relate them with corresponding game systems.
Rule-based languages lie at the core of several areas of central importance to databases and artificial intelligence such as deductive databases and knowledge representation and reasoning. Disjunctive existential rules (a.k.a. disjunctive…
Many efforts have been dedicated to identifying restrictions on ontologies expressed as tuple-generating dependencies (tgds), a.k.a. existential rules, that lead to the decidability for the problem of answering ontology-mediated queries…
Ontology-based query answering (OBQA) asks whether a Boolean conjunctive query is satisfied by all models of a logical theory consisting of a relational database paired with an ontology. The introduction of existential rules (i.e., Datalog…
Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages. In the past few years, a number of rule languages with finite chase have been studied. In this work, we…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism…
Rules complement and extend ontologies on the Semantic Web. We refer to these rules as onto-relational since they combine DL-based ontology languages and Knowledge Representation formalisms supporting the relational data model within the…
We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued…
Description logics are knowledge representation formalisms that provide the formal underpinning of the semantic web and in particular of the $\text{OWL}$ Ontology Web Language. In this paper we investigate the expressive power of logic…
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…
The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check…
Several types of dependencies have been proposed for the static analysis of existential rule ontologies, promising insights about computational properties and possible practical uses of a given set of rules, e.g., in ontology-based query…
We consider an extension of logic programs, called \omega-programs, that can be used to define predicates over infinite lists. \omega-programs allow us to specify properties of the infinite behavior of reactive systems and, in general,…
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…