The core chase, a popular algorithm for answering conjunctive queries (CQs) over existential rules, is guaranteed to terminate and compute a finite universal model whenever one exists, leading to the equivalence of the universal-model-based and the chase-based definitions of finite expansion sets (fes) -- a class of rulesets featuring decidable CQ entailment. In case of non-termination, however, it is non-trivial to define a ''result'' of the core chase, due to its non-monotonicity. This causes complications when dealing with advanced decidability criteria based on the existence of (universal) models of finite treewidth. For these, sufficient chase-based conditions have only been established for weaker, monotonic chase variants. This paper investigates the -- prima facie plausible -- hypothesis that the existence of a treewidth-bounded universal model and the existence of a treewidth-bounded core-chase sequence coincide -- which would conveniently entail decidable CQ entailment whenever the latter holds. Perhaps surprisingly, carefully crafted examples show that both directions of this hypothesized correspondence fail. On a positive note, we are still able to define an aggregation scheme for the infinite core chase that preserves treewidth bounds and produces a finitely universal model, i.e., one that satisfies exactly the entailed CQs. This allows us to prove that the existence of a treewidth-bounded core-chase sequence does warrant decidability of CQ entailment (yet, on other grounds than expected). Hence, for the first time, we are able to define a chase-based notion of bounded treewidth sets of rules that subsumes fes.

Ontology-mediated query answering is concerned with the problem of answering queries over knowledge bases consisting of a database instance and an ontology. While most work in the area focuses on conjunctive queries, navigational queries are gaining increasing attention. In this paper, we investigate the complexity of answering two-way conjunctive regular path queries (CRPQs) over knowledge bases whose ontology is given by a set of guarded existential rules. We first consider the subclass of linear existential rules and show that CRPQ answering is EXPTIME-complete in combined complexity and NL-complete in data complexity, matching the recently established bounds for answering non-conjunctive RPQs. For guarded rules, we provide a non-trivial reduction to the linear case, which allows us to show that the complexity of CRPQ answering is the same as for plain conjunctive queries, namely, 2EXPTIME-complete in combined complexity and PTIME-complete in data complexity.

Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology-Based Query Answering. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure the termination of a breadth-first forward chaining algorithm known as the chase. First, we propose a new tool that allows to extend existing acyclicity conditions ensuring chase termination, while keeping good complexity properties. Second, we consider the extension to existential rules with nonmonotonic negation under stable model semantics and further extend acyclicity results obtained in the positive case.

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Checking satisfiability of temporal constraint networks involves infinite variables domains. We explore a solution based upon finite partitions of infinite domains. Though a straightforward partition results in a sound and complete backtrack, its extension to forward checking is not complete. Using bi-intervals, we obtain sound and complete backtrack and forward checking algorithms. Moreover, we show that bi-intervals used in a hybrid algorithm which also instantiates constraints improve backtrack efficiency.

Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon Sowa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given in terms of positive, conjunctive, existential FOL. We present here a family of extensions of this model, based on rules and constraints, keeping graph homomorphism as the basic operation. We focus on the formal definitions of the different models obtained, including their operational semantics and relationships with FOL, and we analyze the decidability and complexity of the associated problems (consistency and deduction). As soon as rules are involved in reasonings, these problems are not decidable, but we exhibit a condition under which they fall in the polynomial hierarchy. These results extend and complete the ones already published by the authors. Moreover we systematically study the complexity of some particular cases obtained by restricting the form of constraints and/or rules.