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We consider the issue of answering unions of conjunctive queries (UCQs) with disjunctive existential rules and mappings. While this issue has already been well studied from a chase perspective, query rewriting within UCQs has hardly been…
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…
We recently proposed Acceleration Driven Clause Learning (ADCL), a novel calculus to analyze satisfiability of Constrained Horn Clauses (CHCs). Here, we adapt ADCL to disprove termination of transition systems, and we evaluate its…
One of the most interesting questions concerning hierarchical control of discrete-event systems with partial observations is a condition under which the language observability is preserved between the original and the abstracted plant.…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
We derive the necessary and sufficient condition, for a given Polynomial Recurrence Sequence to converge to a given target rational K. By converge, we mean that the Nth term of the sequence, is equal to K, as N tends to positive infinity.…
Transitive closure logic is a known extension of first-order logic obtained by introducing a transitive closure operator. While other extensions of first-order logic with inductive definitions are a priori parametrized by a set of inductive…
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…
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…
We describe a method for proving non-looping non-termination, that is, of term rewriting systems that do not admit looping reductions. As certificates of non-termination, we employ regular (tree) automata.
The objective of this paper is to present general, mechanically verified, refinement rules for reasoning about recursive programs and while loops in the context of concurrency. Unlike many approaches to concurrency, we do not assume that…
In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…
Recent search agents leverage multi-turn reasoning and search tools to achieve strong performance on multi-hop and long-horizon benchmarks. Yet it remains unclear whether they reliably reason across all requirements by tracking, verifying,…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
Restriction is a natural quasi-order on $d$-way tensors. We establish a remarkable aspect of this quasi-order in the case of tensors over a fixed finite field -- namely, that it is a well-quasi-order: it admits no infinite antichains and no…
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…
In this paper, we define two particular forms of non-termination, namely loops and binary chains, in an abstract framework that encompasses term rewriting and logic programming. The definition of loops relies on the notion of compatibility…
We propose a cut-free cyclic system for Transitive Closure Logic (TCL) based on a form of hypersequents, suitable for automated reasoning via proof search. We show that previously proposed sequent systems are cut-free incomplete for basic…
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…