Related papers: The Complexity of Circumscription in DLs
Two major difficulties in using default logics are their intractability and the problem of selecting among multiple extensions. We propose an approach to these problems based on integrating nommonotonic reasoning with plausible reasoning…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
In the context of ontology-mediated querying with description logics (DLs), we study the data complexity of queries in which selected predicates can be closed (OMQCs). We provide a non-uniform analysis, aiming at a classification of the…
In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D,…
Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are…
Many practical problems are characterized by a preference relation over admissible solutions, where preferred solutions are minimal in some sense. For example, a preferred diagnosis usually comprises a minimal set of reasons that is…
In temporal logics, a central question is about the choice of modalities and their relative expressive power, in comparison to the complexity of decision problems such as satisfiability. In this tutorial, we will illustrate the study of…
We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of concept combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC TR, whose semantics is based on the…
We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of…
Concrete domains, especially those that allow to compare features with numeric values, have long been recognized as a very desirable extension of description logics (DLs), and significant efforts have been invested into adding them to usual…
Description logic programs (dl-programs) under the answer set semantics formulated by Eiter {\em et al.} have been considered as a prominent formalism for integrating rules and ontology knowledge bases. A question of interest has been…
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…
The aim of this paper is to show how we can handle the Recognising Textual Entailment (RTE) task by using Description Logics (DLs). To do this, we propose a representation of natural language semantics in DLs inspired by existing…
This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
We analyze the computational complexity of admissibility and unifiability with parameters in transitive modal logics. The class of cluster-extensible (clx) logics was introduced in the first part of this series of papers. We completely…
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…
In this paper syntactic objects---concept constructors called part restrictions which realize rational grading are considered in Description Logics (DLs). Being able to convey statements about a rational part of a set of successors, part…
Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates…
We start by defining an approach to non-monotonic probabilistic reasoning in terms of non-monotonic categorical (true-false) reasoning. We identify a type of non-monotonic probabilistic reasoning, akin to default inheritance, that is…