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Description Logic


Conservative Extensions in Horn Description Logics with Inverse Roles

Journal of Artificial Intelligence Research

We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative extensions, defined by requiring that the answers to all conjunctive queries are left unchanged, and deductive conservative extensions, which require that the entailed concept inclusions, role inclusions, and functionality assertions do not change. Upper bounds for query conservative extensions are particularly challenging because characterizations in terms of unbounded homomorphisms between universal models, which are the foundation of the standard approach to establishing decidability, fail in the presence of inverse roles. We resort to a characterization that carefully mixes unbounded and bounded homomorphisms and enables a decision procedure that combines tree automata and a mosaic technique. Our main results are that query conservative extensions are 2ExpTime-complete in all DLs between ELI and Horn-ALCHIF and between Horn-ALC and Horn-ALCHIF, and that deductive conservative extensions are 2ExpTime-complete in all DLs between ELI and ELHIF . The same results hold for inseparability and entailment.


CQE in Description Logics Through Instance Indistinguishability (extended version)

arXiv.org Artificial Intelligence

We study privacy-preserving query answering in Description Logics (DLs). Specifically, we consider the approach of controlled query evaluation (CQE) based on the notion of instance indistinguishability. We derive data complexity results for query answering over DL-Lite$_{\mathcal{R}}$ ontologies, through a comparison with an alternative, existing confidentiality-preserving approach to CQE. Finally, we identify a semantically well-founded notion of approximated query answering for CQE, and prove that, for DL-Lite$_{\mathcal{R}}$ ontologies, this form of CQE is tractable with respect to data complexity and is first-order rewritable, i.e., it is always reducible to the evaluation of a first-order query over the data instance.


Reasoning about Typicality and Probabilities in Preferential Description Logics

arXiv.org Artificial Intelligence

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) D, whose intuitive meaning is that "normally/typically Cs are also Ds". This extension is based on a minimal model semantics corresponding to a notion of rational closure, built upon preferential models. We recall the basic concepts underlying preferential Description Logics. We also present two extensions of the preferential semantics: on the one hand, we consider probabilistic extensions, based on a distributed semantics that is suitable for tackling the problem of commonsense concept combination, on the other hand, we consider other strengthening of the rational closure semantics and construction to avoid the so called "blocking of property inheritance problem".


Querying and Repairing Inconsistent Prioritized Knowledge Bases: Complexity Analysis and Links with Abstract Argumentation

arXiv.org Artificial Intelligence

In this paper, we explore the issue of inconsistency handling over prioritized knowledge bases (KBs), which consist of an ontology, a set of facts, and a priority relation between conflicting facts. In the database setting, a closely related scenario has been studied and led to the definition of three different notions of optimal repairs (global, Pareto, and completion) of a prioritized inconsistent database. After transferring the notions of globally-, Pareto- and completion-optimal repairs to our setting, we study the data complexity of the core reasoning tasks: query entailment under inconsistency-tolerant semantics based upon optimal repairs, existence of a unique optimal repair, and enumeration of all optimal repairs. Our results provide a nearly complete picture of the data complexity of these tasks for ontologies formulated in common DL-Lite dialects. The second contribution of our work is to clarify the relationship between optimal repairs and different notions of extensions for (set-based) argumentation frameworks. Among our results, we show that Pareto-optimal repairs correspond precisely to stable extensions (and often also to preferred extensions), and we propose a novel semantics for prioritized KBs which is inspired by grounded extensions and enjoys favourable computational properties. Our study also yields some results of independent interest concerning preference-based argumentation frameworks.


Satisfiability and Query Answering in Description Logics with Global and Local Cardinality Constraints

arXiv.org Artificial Intelligence

We introduce and investigate the expressive description logic (DL) ALCSCC++, in which the global and local cardinality constraints introduced in previous papers can be mixed. On the one hand, we prove that this does not increase the complexity of satisfiability checking and other standard inference problems. On the other hand, the satisfiability problem becomes undecidable if inverse roles are added to the languages. In addition, even without inverse roles, conjunctive query entailment in this DL turns out to be undecidable. We prove that decidability of querying can be regained if global and local constraints are not mixed and the global constraints are appropriately restricted. The latter result is based on a locally-acyclic model construction, and it reduces query entailment to ABox consistency in the restricted setting, i.e., to ABox consistency w.r.t. restricted cardinality constraints in ALCSCC, for which we can show an ExpTime upper bound.


Polynomial Rewritings from Expressive Description Logics with Closed Predicates to Variants of Datalog

arXiv.org Artificial Intelligence

In many scenarios, complete and incomplete information coexist. For this reason, the knowledge representation and database communities have long shown interest in simultaneously supporting the closed- and the open-world views when reasoning about logic theories. Here we consider the setting of querying possibly incomplete data using logic theories, formalized as the evaluation of an ontology-mediated query (OMQ) that pairs a query with a theory, sometimes called an ontology, expressing background knowledge. This can be further enriched by specifying a set of closed predicates from the theory that are to be interpreted under the closed-world assumption, while the rest are interpreted with the open-world view. In this way we can retrieve more precise answers to queries by leveraging the partial completeness of the data. The central goal of this paper is to understand the relative expressiveness of OMQ languages in which the ontology is written in the expressive Description Logic (DL) ALCHOI and includes a set of closed predicates. We consider a restricted class of conjunctive queries. Our main result is to show that every query in this non-monotonic query language can be translated in polynomial time into Datalog with negation under the stable model semantics. To overcome the challenge that Datalog has no direct means to express the existential quantification present in ALCHOI, we define a two-player game that characterizes the satisfaction of the ontology, and design a Datalog query that can decide the existence of a winning strategy for the game. If there are no closed predicates, that is in the case of querying a plain ALCHOI knowledge base, our translation yields a positive disjunctive Datalog program of polynomial size. To the best of our knowledge, unlike previous translations for related fragments with expressive (non-Horn) DLs, these are the first polynomial time translations.


Game Description Logic with Integers: A GDL Numerical Extension

arXiv.org Artificial Intelligence

Many problems can be viewed as games, where one or more agents try to ensure that certain objectives hold no matter t he behavior from the environment and other agents. In recent years, a num ber of logical formalisms have been proposed for specifying games amo ng which the Game Description Language (GDL) was established as the o fficial language for General Game Playing. Although numbers are rec urring in games, the description of games with numerical features in G DL requires the enumeration from all possible numeric values and the rel ation among them. Thereby, in this paper, we introduce the Game Descript ion Logic with Integers (GDLZ) to describe games with numerical varia bles, numerical parameters, as well as to perform numerical compari sons. We compare our approach with GDL and show that when describing t he same game, GDLZ is more compact.


An Introduction to Artificial Intelligence Applied to Multimedia

#artificialintelligence

In this chapter, we give an introduction to symbolic artificial intelligence (AI) and discuss its relation and application to multimedia. We begin by defining what symbolic AI is, what distinguishes it from non-symbolic approaches, such as machine learning, and how it can used in the construction of advanced multimedia applications. We then introduce description logic (DL) and use it to discuss symbolic representation and reasoning. DL is the logical underpinning of OWL, the most successful family of ontology languages. After discussing DL, we present OWL and related Semantic Web technologies, such as RDF and SPARQL.


Statistical EL is ExpTime-complete

arXiv.org Artificial Intelligence

We show that consistency of Statistical EL knowledge bases, as defined by Penaloza and Potyka in SUM 2017 [4] is ExpTime-hard. Together with the existing ExpTime upper bound by Baader in FroCos 2017 [1], the result leads to the ExpTime-completeness of the mentioned logic. Our proof goes via a reduction from consistency of EL extended with an atomic negation, which is known to be equivalent to the well-known ExpTime-complete description logic ALC.


Description Logics

Journal of Artificial Intelligence Research

Over the past two decades, Description Logics (DLs) have grown tremendously in popularity both within the AI community and beyond, due to the balanced trade-off they offer between expressivity and complexity of reasoning. The current success of DLs is the result of many years of rigorous research carried out by the DL community, which has yielded not only beautiful theoretical results but also powerful systems and im- portant practical applications. Notably, DLs provide the logical underpinning of ontology languages (including the W3C standard OWL), making them relevant to a variety of application domains, such as semantic web, medical informatics, life sciences, e-commerce, etc. The objective of this special track is to showcase the best of current DL research. The Track received 17 submissions of which the following seven papers for publication in the special track.