Related papers: Checking Chase Termination over Ontologies of Exis…
Independence logic cannot be effectively axiomatized. However, first-order consequences of independence logic sentences can be axiomatized. In this article we give an explicit axiomatization and prove that it is complete in this sense. The…
Recently, there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The presence of function symbols in the program may render the ground instantiation infinite, and finiteness…
It is well-known that Choice and Regularity are independent of each other but have important common consequences of logical character (reflection principles, representations of classes by sets, etc.). We explain this phenomenon by isolating…
Ranking individuals based on their performance in different coalitions is a problem emerging in various domains (teams sports, scientific evaluation, argumentation, etc.). Often, for practical reasons, the number of comparable coalitions is…
A conjunctive query (CQ) is semantically acyclic if it is equivalent to an acyclic one. Semantic acyclicity has been studied in the constraint-free case, and deciding whether a query enjoys this property is NP-complete. However, in case the…
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…
In heap-based languages, knowing that a variable x points to an acyclic data structure is useful for analyzing termination: this information guarantees that the depth of the data structure to which x points is greater than the depth of the…
Sound exhaustiveness checking of pattern-matching is an essential feature of functional programming languages, and OCaml supports it for GADTs. However this check is incomplete, in that it may fail to detect that a pattern can match no…
A cyclic proof system generalises the standard notion of a proof as a finite tree of locally sound inferences by allowing proof objects to be potentially infinite. Regular infinite proofs can be finitely represented as graphs. To preclude…
In this paper we deal with verification of safety properties of parameterized systems with a tree topology. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which…
Linearizability is a standard correctness criterion for concurrent algorithms, typically proved by establishing the algorithms' linearization points. However, relying on linearization points leads to proofs that are…
This works is motivated by a real-world case study where it is necessary to integrate and relate existing ontologies through meta- modelling. For this, we introduce the Description Logic ALCQM which is obtained from ALCQ by adding…
Reasoning about exceptions in ontologies is nowadays one of the challenges the description logics community is facing. The paper describes a preferential approach for dealing with exceptions in Description Logics, based on the rational…
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…
The reflection principle is the statement that if a sentence is provable then it is true. Reflection principles have been studied for first-order theories, but they also play an important role in propositional proof complexity. In this…
We propose analyzing conditional reasoning by appeal to a notion of intervention on a simulation program, formalizing and subsuming a number of approaches to conditional thinking in the recent AI literature. Our main results include a…
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
We give sound and complete axiomatizations for XPath with data tests by "equality" or "inequality", and containing the single "child" axis. This data-aware logic predicts over data trees, which are tree-like structures whose every node…
The chaotic hypothesis discussed in [GC1] is tested experimentally in a simple conduction model. Besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which, as…
Dependence logic, introduced in [8], cannot be axiomatized. However, first-order consequences of dependence logic sentences can be axiomatized, and this is what we shall do in this paper. We give an explicit axiomatization and prove the…