Related papers: Normalisations of Existential Rules: Not so Innocu…
A knowledge system S describing a part of real world does in general not contain complete information. Reasoning with incomplete information is prone to errors since any belief derived from S may be false in the present state of the world.…
When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
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…
We consider existential rules (aka Datalog+) as a formalism for specifying ontologies. In recent years, many classes of existential rules have been exhibited for which conjunctive query (CQ) entailment is decidable. However, most of these…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
The chase is a sound and complete algorithm for conjunctive query answering over ontologies of existential rules with equality. To enable its effective use, we can apply acyclicity notions; that is, sufficient conditions that guarantee…
In this research, new concepts of existential granules that determine themselves are invented, and are characterized from algebraic, topological, and mereological perspectives. Existential granules are those that determine themselves…
The chase is a fundamental algorithm with ubiquitous uses in database theory. Given a database and a set of existential rules (aka tuple-generating dependencies), it iteratively extends the database to ensure that the rules are satisfied in…
Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or…
We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments…
The rules associated with propositional logic programs and the stable model semantics are not expressive enough to let one write concise programs. This problem is alleviated by introducing some new types of propositional rules. Together…
The disjunctive restricted chase is a sound and complete procedure for solving boolean conjunctive query entailment over knowledge bases of disjunctive existential rules. Alas, this procedure does not always terminate and checking if it…
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…
An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be…
Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
In physics, there is the prevailing intuition that we are part of a unique external world, and that the goal of physics is to understand and describe this world. This assumption of the fundamentality of objective reality is often seen as a…
We study regular expressions that use variables, or parameters, which are interpreted as alphabet letters. We consider two classes of languages denoted by such expressions: under the possibility semantics, a word belongs to the language if…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…