Related papers: Conservative Extensions for Existential Rules
Ontological query answering is the problem of answering queries in the presence of schema constraints representing the domain of interest. Datalog+/- is a common family of languages for schema constraints, including tuple-generating…
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical…
The chase is a fundamental algorithm with ubiquitous uses in database theory. Given a database and a set of existential rules (aka tuple-generating dependencies), it iteratively extends the database to ensure that the rules are satisfied in…
We consider the Cauchy problem for a degenerate fractional conservation laws driven by a noise. In particular, making use of an adapted kinetic formulation, a result of existence and uniqueness of solution is established. Moreover, a…
We address the problem of minimal-change integrity maintenance in the context of integrity constraints in relational databases. We assume that integrity-restoration actions are limited to tuple deletions. We identify two basic computational…
We investigate the problem of deciding whether a system of linear equations, together with divisibility conditions on the variables, has a solution over holomorphy subrings of global fields. We obtain decidability results when we allow…
This paper examines two related problems that are central to developing an autonomous decision-making agent, such as a robot. Both problems require generating structured representafions from a database of unstructured declarative knowledge…
We call a first-order formula one-dimensional if its every maximal block of existential (universal) quantifiers leaves at most one variable free. We consider the one-dimensional restrictions of the guarded fragment, GF, and the tri-guarded…
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…
A default theory can be characterized by its sets of plausible conclusions, called its extensions. But, due to the theoretical complexity of Default Logic (Sigma_2p-complete), the problem of finding such an extension is very difficult if…
An algebraic telic problem is a decision problem in $\textsf{NP}_\mathbb{R}$ formalizing finite-time reachability questions for one-dimensional dynamical systems. We prove that the existence of "natural" mapping reductions between algebraic…
All known structural extensions of the substructural logic $\mathsf{FL_e}$, Full Lambek calculus with exchange/commutativity, (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$-equations)…
Let T be an algebraically bounded theory. We consider the $L(\bar\delta)$-expansions of T by a tuple $\bar \delta$ of derivations (which may be commuting or not). We investigate the model completion of either of the above theories, whose…
We prove that one cannot algorithmically decide whether a finitely presented $\mathbb{Z}$-extension admits a finitely generated base group, and we use this fact to prove the undecidability of the BNS invariant. Furthermore, we show the…
Ontology-based query answering with existential rules is well understood and implemented for positive queries, in particular conjunctive queries. The situation changes drastically for queries with negation, where there is no agreed-upon…
In this study we are concerned with the general problem of choosing from a set of endangered species T a subset S of k species to protect as a priority. Here, the interest to protect the species of S is assessed by the resulting expected…
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 consider the complexity of the open-world query answering problem, where we wish to determine certain answers to conjunctive queries over incomplete datasets specified by an initial set of facts and a set of guarded TGDs. This problem…
Every simplest potential conservation law of any (1+1)-dimensional linear evolution equation of even order proves induced by a local conservation law of the same equation. This claim is true also for linear simplest potential conservation…