Related papers: Union and Intersection of all Justifications
Logic-based approaches to AI have the advantage that their behavior can in principle be explained with the help of proofs of the computed consequences. For ontologies based on Description Logic (DL), we have put this advantage into practice…
In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology, which can be formulated in a description logic (DL) or using existential rules. In the literature, there…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
The intersection type assignment system has been designed directly as deductive system for assigning formulae of the implicative and conjunctive fragment of the intuitionistic logic to terms of lambda-calculus. But its relation with the…
Inconsistency handling is an important issue in knowledge management. Especially in ontology engineering, logical inconsistencies may occur during ontology construction. A natural way to reason with an inconsistent ontology is to utilize…
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for…
Unification in Description Logics has been introduced as a means to detect redundancies in ontologies. We try to extend the known decidability results for unification in the Description Logic $\mathcal{EL}$ to disunification since negative…
We give an optimal (EXPTIME), sound and complete tableau-based algorithm for deciding satisfiability for propositional dynamic logic with converse (CPDL) which does not require the use of analytic cut. Our main contribution is a sound…
We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such…
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…
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
Consequence-based calculi are a family of reasoning algorithms for description logics (DLs), and they combine hypertableau and resolution in a way that often achieves excellent performance in practice. Up to now, however, they were proposed…
Ontological queries are evaluated against an ontology rather than directly on a database. The evaluation and optimization of such queries is an intriguing new problem for database research. In this paper we discuss two important aspects of…
For any simple digraph $D$ we offer a new proof for the intersection number of its middle digraph, $M(D)$; while doing so we also solve for the intersection number when $D$ has loops. In addition, a new transformation, the union of $D$ and…
Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the…
Decision lists (DLs) find a wide range of uses for classification problems in Machine Learning (ML), being implemented in a number of ML frameworks. DLs are often perceived as interpretable. However, building on recent results for decision…
Modern ontology debugging methods allow efficient identification and localization of faulty axioms defined by a user while developing an ontology. The ontology development process in this case is characterized by rather frequent and regular…
In this paper, it is shown that the solutions of general differentiable constrained optimization problems can be viewed as asymptotic solutions to sets of Ordinary Differential Equations (ODEs). The construction of the ODE associated to the…
Multiple logic-based reconstructions of conceptual data modelling languages such as EER, UML Class Diagrams, and ORM exist. They mainly cover various fragments of the languages and none are formalised such that the logic applies…