Related papers: On the k-Boundedness for Existential Rules
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…
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…
Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove three related problems are decidable. We apply one result to…
We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation…
The chase procedure, an algorithm proposed 25+ years ago to fix constraint violations in database instances, has been successfully applied in a variety of contexts, such as query optimization, data exchange, and data integration. Its…
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…
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…
Motivated by the success of bounded model checking framework for finite state machines, Ouaknine and Worrell proposed a time-bounded theory of real-time verification by claiming that restriction to bounded-time recovers decidability for…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…
The decidability of axiomatic extensions of the modal logic K with modal reduction principles, i.e. axioms of the form $\Diamond^{k} p \rightarrow \Diamond^{n} p$, has remained a long-standing open problem. In this paper, we make…
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 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…
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…
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…
Extensive research in the field of ontology-based query answering has led to the identification of numerous fragments of existential rules (also known as tuple-generating dependencies) that exhibit decidable answering of atomic and…
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…
Bounded-rate multi-mode systems are hybrid systems that can switch among a finite set of modes. Its dynamics is specified by a finite number of real-valued variables with mode-dependent rates that can vary within given bounded sets. Given…
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…
We present CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. Even for decidable constraint systems, satisfiability and Model Checking problem of such…
The undecidability of basic decision problems for general FIFO machines such as reachability and unboundedness is well-known. In this paper, we provide an underapproximation for the general model by considering only runs that are…