Related papers: Characterizing Boundedness in Chase Variants
Query answering under existential rules -- implications with existential quantifiers in the head -- is known to be decidable when imposing restrictions on the rule bodies such as frontier-guardedness [BLM10, BLMS11]. Query answering is also…
The chase is a widely implemented approach to reason with tuple-generating dependencies (tgds), used in data exchange, data integration, and ontology-based query answering. However, it is merely a semi-decision procedure, which may fail to…
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…
In this paper we take closer look at recent developments for the chase procedure, and provide additional results. Our analysis allows us create a taxonomy of the chase variations and the properties they satisfy. Two of the most central…
Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases. This problem can be solved using the chase algorithm, which extends the given set of…
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 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…
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…
We study the interaction of views, queries, and background knowledge in the form of existential rules. The motivating questions concern monotonic determinacy of a query using views w.r.t. rules, which refers to the ability to recover the…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
We study reasoning with existential rules to perform query answering over streams of data. On static databases, this problem has been widely studied, but its extension to rapidly changing data has not yet been considered. To bridge this…
The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded…
There are many types of automata and grammar models that have been studied in the literature, and for these models, it is common to determine whether certain problems are decidable. One problem that has been difficult to answer throughout…
Machine Learning explainability techniques have been proposed as a means of `explaining' or interrogating a model in order to understand why a particular decision or prediction has been made. Such an ability is especially important at a…
Open-world query answering is the problem of deciding, given a set of facts, conjunction of constraints, and query, whether the facts and constraints imply the query. This amounts to reasoning over all instances that include the facts and…
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…
We study the termination problem of the chase algorithm, a central tool in various database problems such as the constraint implication problem, Conjunctive Query optimization, rewriting queries using views, data exchange, and data…
The existential k-pebble game characterizes the expressive power of the existential-positive k-variable fragment of first-order logic on finite structures. The winner of the existential k-pebble game on two given finite structures can be…
The chase procedure, originally introduced for checking implication of database constraints, and later on used for computing data exchange solutions, has recently become a central algorithmic tool in rule-based ontological reasoning. In…
One measure of the complexity of a first-order theory, and similarly a type, is the complexity of the formulas required to axiomatize it. We say a theory is bounded if there is an axiomatization involving only $\forall_n$-formulas for some…