Related papers: Connected Components and Disjunctive Existential R…
These lecture notes survey the emerging area of Universal Proof Theory, which investigates general questions about the existence, equivalence, and characterization of good proof systems for broad classes of logics. In particular, the notes…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
Machine reading comprehension with unanswerable questions is a new challenging task for natural language processing. A key subtask is to reliably predict whether the question is unanswerable. In this paper, we propose a unified model,…
We study the enumeration of answers to Unions of Conjunctive Queries (UCQs) with optimal time guarantees. More precisely, we wish to identify the queries that can be solved with linear preprocessing time and constant delay. Despite the…
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…
Approximate Membership Query structures (AMQs) rely on randomisation for time- and space-efficiency, while introducing a possibility of false positive and false negative answers. Correctness proofs of such structures involve subtle…
We consider a modification of the Quantifier Elimination (QE) problem called Partial QE (PQE). In PQE, only a small part of the formula is taken out of the scope of quantifiers. The appeal of PQE is that many verification problems, e.g.…
We propose an algorithm for answering conjunctive queries with negation, where the negated relations have bounded degree. Its data complexity matches that of the best known algorithms for the positive subquery of the input query and is…
This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically…
Fuzzy Description Logics (DLs) provide a means for representing vague knowledge about an application domain. In this paper, we study fuzzy extensions of conjunctive queries (CQs) over the DL $\mathcal{SROIQ}$ based on finite chains of…
Rewriting Induction (RI) is a principle to prove that an equation over terms is an inductive theorem of a rewrite system, i.e., that any ground instance of the equation is a theorem of the rewrite system. RI has been adapted to several…
In this paper, we consider existential rules, an expressive formalism well suited to the representation of ontological knowledge and data-to-ontology mappings in the context of ontology-based data integration. The chase is a fundamental…
The topic of this paper is the Finiteness Conjecture for minimally unsatisfiable clause-sets (MUs), stating that for each fixed deficiency (number of clauses minus number of variables) there are only finitely many patterns, given a certain…
The logic of hybrid MKNF (minimal knowledge and negation as failure) is a powerful knowledge representation language that elegantly pairs ASP (answer set programming) with ontologies. Disjunctive rules are a desirable extension to normal…
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has…
We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions. Our methodology is category-theoretical in nature, where the…
We introduce a novel approach that exploits the intersection of quantum computing, machine learning and reduced density matrix functional theory to leverage the potential of quantum computing to improve simulations of interacting quantum…
Regular expressions with capture variables, also known as "regex formulas," extract relations of spans (interval positions) from text. These relations can be further manipulated via Relational Algebra as studied in the context of document…