scholarly journals Computing and Explaining Query Answers over Inconsistent DL-Lite Knowledge Bases

2019 ◽  
Vol 64 ◽  
pp. 563-644 ◽  
Author(s):  
Meghyn Bienvenu ◽  
Camille Bourgaux ◽  
François Goasdoué
Keyword(s):  
Description Logic ◽  
Optimization Problems ◽  
Knowledge Bases ◽  
Query Answering ◽  
Practical Approach ◽  
Propositional Satisfiability ◽  
Data Complexity ◽  
Sat Problem ◽  
Computational Properties

Several inconsistency-tolerant semantics have been introduced for querying inconsistent description logic knowledge bases. The first contribution of this paper is a practical approach for computing the query answers under three well-known such semantics, namely the AR, IAR and brave semantics, in the lightweight description logic DL-LiteR. We show that query answering under the intractable AR semantics can be performed efficiently by using IAR and brave semantics as tractable approximations and encoding the AR entailment problem as a propositional satisfiability (SAT) problem. The second issue tackled in this work is explaining why a tuple is a (non-)answer to a query under these semantics. We define explanations for positive and negative answers under the brave, AR and IAR semantics. We then study the computational properties of explanations in DL-LiteR. For each type of explanation, we analyze the data complexity of recognizing (preferred) explanations and deciding if a given assertion is relevant or necessary. We establish tight connections between intractable explanation problems and variants of SAT, enabling us to generate explanations by exploiting solvers for Boolean satisfaction and optimization problems. Finally, we empirically study the efficiency of our query answering and explanation framework using a benchmark we built upon the well-established LUBM benchmark.

An Improved Set-based Reasoner for the Description Logic 𝒟ℒD4,׆

2021 ◽  
Vol 178 (4) ◽  
pp. 315-346
Author(s):  
Domenico Cantone ◽  
Marianna Nicolosi-Asmundo ◽  
Daniele Francesco Santamaria
Keyword(s):  
Semantic Web ◽  
Set Theory ◽  
Description Logic ◽  
Knowledge Bases ◽  
Query Answering ◽  
Conjunctive Query ◽  
Classification Problems ◽  
Previous Version ◽  
Decidable Fragment ◽  
Stratified Set

We present a KE-tableau-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic 𝒟ℒ〈4LQSR,×〉(D) (𝒟ℒD4,×, for short). Our application solves the main TBox and ABox reasoning problems for 𝒟ℒD4,×. In particular, it solves the consistency and the classification problems for 𝒟ℒD4,×-knowledge bases represented in set-theoretic terms, and a generalization of the Conjunctive Query Answering problem in which conjunctive queries with variables of three sorts are admitted. The reasoner, which extends and improves a previous version, is implemented in C++. It supports 𝒟ℒD4,×-knowledge bases serialized in the OWL/XML format and it admits also rules expressed in SWRL (Semantic Web Rule Language).

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

2020 ◽  
Author(s):  
Meghyn Bienvenu ◽  
Camille Bourgaux
Keyword(s):  
Complexity Analysis ◽  
Knowledge Bases ◽  
Data Complexity ◽  
The Core ◽  
Inconsistency Handling ◽  
Definition Of ◽  
Priority Relation ◽  
Inconsistent Database ◽  
The Relationship ◽  
Computational Properties

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.

scholarly journals Conjunctive Query Answering for the Description Logic SHIQ

2008 ◽  
Vol 31 ◽  
pp. 157-204 ◽  
Author(s):  
B. Glimm ◽  
C. Lutz ◽  
I. Horrocks ◽  
U. Sattler
Keyword(s):  
Description Logic ◽  
Query Language ◽  
Description Logics ◽  
Knowledge Bases ◽  
Deterministic Algorithm ◽  
Query Answering ◽  
Conjunctive Query ◽  
Conjunctive Queries ◽  
Complexity Bounds ◽  
Double Exponential

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP.

scholarly journals Answering Fuzzy Queries over Fuzzy DL-Lite Ontologies

2022 ◽  
pp. 1-30
Author(s):  
GABRIELLA PASI ◽  
RAFAEL PEÑALOZA
Keyword(s):  
Fuzzy Logic ◽  
Domain Knowledge ◽  
Description Logic ◽  
Classical Case ◽  
Point Of View ◽  
Query Answering ◽  
Data Complexity ◽  
Conjunctive Query ◽  
Triangular Norm ◽  
Mathematical Fuzzy Logic

Abstract A prominent problem in knowledge representation is how to answer queries taking into account also the implicit consequences of an ontology representing domain knowledge. While this problem has been widely studied within the realm of description logic ontologies, it has been surprisingly neglected within the context of vague or imprecise knowledge, particularly from the point of view of mathematical fuzzy logic. In this paper, we study the problem of answering conjunctive queries and threshold queries w.r.t. ontologies in fuzzy DL-Lite. Specifically, we show through a rewriting approach that threshold query answering w.r.t. consistent ontologies remains in ${AC}^{0}$ in data complexity, but that conjunctive query answering is highly dependent on the selected triangular norm, which has an impact on the underlying semantics. For the idempotent Gödel t-norm, we provide an effective method based on a reduction to the classical case.

Boolean Role Inclusions in DL-Lite With and Without Time

2020 ◽  
Author(s):  
Roman Kontchakov ◽  
Vladislav Ryzhikov ◽  
Frank Wolter ◽  
Michael Zakharyaschev
Keyword(s):  
Description Logic ◽  
Expressive Power ◽  
Necessary Condition ◽  
Data Complexity ◽  
Temporal Dimension ◽  
Complexity Level ◽  
Primitive Recursion ◽  
Lower Complexity ◽  
Computational Properties

Traditionally, description logic has focused on representing and reasoning about classes rather than relations (roles), which has been justified by the deterioration of the computational properties if expressive role inclusions are added. The situation is even worse in the temporalised setting, where monodicity is viewed as an almost necessary condition for decidability. We take a fresh look at the description logic DL-Lite with expressive role inclusions, both with and without a temporal dimension. While we confirm that full Boolean expressive power on roles leads to FO^2-like behaviour in the atemporal case and undecidability in the temporal case, we show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to much lower complexity in the atemporal case and to decidability (and ExpSpace-completeness) in the temporal case, even if one admits full Booleans on concepts. The latter result is one of very few instances breaking the monodicity barrier in temporal FO. This is also reflected on the data complexity level, where we obtain new rewritability results into FO with relational primitive recursion and FO with unary divisibility predicates.

Secrecy-Preserving Reasoning and Query Answering in Probabilistic Description Logic Knowledge Bases

10.29007/npd4 ◽  
2018 ◽  
Author(s):  
Gopalakrishnan Krishnasamy Sivaprakasam ◽  
Adrienne Raglin ◽  
Douglas Summers-Stay ◽  
Giora Slutzki
Keyword(s):  
Probabilistic Model ◽  
Description Logic ◽  
Knowledge Bases ◽  
Query Answering ◽  
Decomposition Algorithm ◽  
Probabilistic Description ◽  
Recursive Query ◽  
Finite Set ◽  
The Given

In this paper we study Secrecy-Preserving Query Answering problem underthe OpenWorld Assumption (OWA) for Prob-EL>0;=1 Knowledge Bases(KBs). We have designed a tableau procedure to compute a semi model Mover the given KB which eventually is equivalent to a probabilistic modelto KB. Given a secrecy set S, which is a finite set of assertions, wecompute a function E, called an envelope of S, which assigns a set E() ofassertions to each world in the semi modal M. E provides logical protection to the secrecy set S against the reasoning of a querying agent. Once the semi model M and an envelope E are computed, we define the secrecy-preserving semi model ME.Based on the information available in ME, assertional queries with probabilisticoperators can be answered eciently while preserving secrecy. Tothe best of our knowledge, this work is first one studying secrecy-preservingreasoning in description logic augmented with probabilistic operators. Whenthe querying agent asks a query q, the reasoner answers “Yes” if informationabout q is available in ME; otherwise, the reasoner answers “Unknown”. Beingable to answer “Unknown” plays a key role in protecting secrecy underOWA. Since we are not computing all the consequences of the knowledgebase, answers to the queries based on just secrecy-preserving semi modelME could be erroneous. To fix this problem, we further augment our algorithmsby providing recursive query decomposition algorithm to make thequery answering procedure foolproof.1

Datalog Rewritability and Data Complexity of ALCHOIF with Closed Predicates

2020 ◽  
Author(s):  
Tomasz Gogacz ◽  
Sanja Lukumbuzya ◽  
Magdalena Ortiz ◽  
Mantas Šimkus
Keyword(s):  
Description Logic ◽  
Answer Set Programming ◽  
Query Answering ◽  
Stable Model ◽  
Data Complexity ◽  
First Order ◽  
Time Translation ◽  
Np Complete ◽  
Ontology Languages

We study the relative expressiveness of ontology-mediated queries (OMQs) formulated in the expressive Description Logic ALCHOIF extended with closed predicates. In particular, we present a polynomial-time translation from OMQs into Datalog with negation under the stable model semantics, the formalism that underlies Answer Set Programming. This is a novel and non-trivial result: the considered OMQs are not only non-monotonic but also feature a tricky combination of nominals, inverse roles, and role functionality. We start with atomic queries and then lift our approach to a large class of first-order queries where quantification is “guarded” by closed predicates. Our translation is based on a characterization of the query answering problem via integer programming, and a specially crafted program in Datalog with negation that finds solutions to dynamically generated systems of integer inequalities. As an important by-product of our translation, we get that the query answering problem is co-NP-complete in data complexity for the considered class of OMQs. Thus, answering these OMQs in the presence of closed predicates is not harder than answering them in the standard setting. This is not obvious as closed predicates are known to increase data complexity for some existing ontology languages.

scholarly journals Answering Conjunctive Regular Path Queries over Guarded Existential Rules

2017 ◽  
Author(s):  
Jean-François Baget ◽  
Meghyn Bienvenu ◽  
Marie-Laure Mugnier ◽  
Michael Thomazo
Keyword(s):  
Knowledge Bases ◽  
Query Answering ◽  
Linear Case ◽  
Data Complexity ◽  
Conjunctive Queries ◽  
Regular Path ◽  
Regular Path Queries ◽  
Path Queries

Ontology-mediated query answering is concerned with the problem of answering queries over knowledge bases consisting of a database instance and an ontology. While most work in the area focuses on conjunctive queries, navigational queries are gaining increasing attention. In this paper, we investigate the complexity of answering two-way conjunctive regular path queries (CRPQs) over knowledge bases whose ontology is given by a set of guarded existential rules. We first consider the subclass of linear existential rules and show that CRPQ answering is EXPTIME-complete in combined complexity and NL-complete in data complexity, matching the recently established bounds for answering non-conjunctive RPQs. For guarded rules, we provide a non-trivial reduction to the linear case, which allows us to show that the complexity of CRPQ answering is the same as for plain conjunctive queries, namely, 2EXPTIME-complete in combined complexity and PTIME-complete in data complexity.

scholarly journals Reverse Engineering Queries in Ontology-Enriched Systems: The Case of Expressive Horn Description Logic Ontologies

2018 ◽  
Author(s):  
Víctor Gutiérrez-Basulto ◽  
Jean Christoph Jung ◽  
Leif Sabellek
Keyword(s):  
Reverse Engineering ◽  
Knowledge Base ◽  
Description Logic ◽  
Knowledge Bases ◽  
Query Answering ◽  
Conjunctive Queries ◽  
Complexity Bounds ◽  
Query By Example

We introduce the query-by-example (QBE) paradigm for query answering in the presence of ontologies. Intuitively, QBE permits non-expert users to explore the data by providing examples of the information they (do not) want, which the system then generalizes into a query. Formally, we study the following question: given a knowledge base and sets of positive and negative examples, is there a query that returns all positive but none of the negative examples?  We focus on description logic knowledge bases with ontologies formulated in Horn-ALCI and (unions of) conjunctive queries. Our main contributions are characterizations, algorithms and tight complexity bounds for QBE.  

scholarly journals Temporal Minimal-World Query Answering over Sparse ABoxes

2021 ◽  
pp. 1-36
Author(s):  
STEFAN BORGWARDT ◽  
WALTER FORKEL ◽  
ALISA KOVTUNOVA
Keyword(s):  
Real World ◽  
Description Logic ◽  
Medical Data ◽  
Query Answering ◽  
Closed Domain ◽  
Data Complexity ◽  
Temporal Dimension ◽  
Health Records ◽  
Closed World ◽  
Real World Applications

Abstract Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge. For querying the absence of information, however, there exist only few ontology-based approaches. Moreover, these proposals conflate the closed-domain and closed-world assumption and, therefore, are not suited to deal with the anonymous objects that are common in ontological reasoning. Many real-world applications, like processing electronic health records, also contain a temporal dimension and require efficient reasoning algorithms. Moreover, since medical data are not recorded on a regular basis, reasoners must deal with sparse data with potentially large temporal gaps. Our contribution consists of two main parts: In the first part, we introduce a new closed-world semantics for answering conjunctive queries (CQs) with negation over ontologies formulated in the description logic $${\mathcal E}{\mathcal L}{{\mathcal H}_ \bot }$$ , which is based on the minimal canonical model. We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity. In the second part, we extend this minimal-world semantics for answering metric temporal CQs with negation over the lightweight temporal logic and obtain similar rewritability and complexity results.

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