scholarly journals Worst-Case Optimal Querying of Very Expressive Description Logics with Path Expressions and Succinct Counting

2019 ◽  
Author(s):  
Bartosz Bednarczyk ◽  
Sebastian Rudolph
Keyword(s):  
Description Logics ◽  
Order Logic ◽  
Conjunctive Query ◽  
Cardinality Constraints ◽  
Worst Case ◽  
First Order ◽  
Regular Path ◽  
Regular Path Queries ◽  
Carry Over ◽  
Path Queries

Among the most expressive knowledge representation formalisms are the description logics of the Z family. For well-behaved fragments of ZOIQ, entailment of positive two-way regular path queries is well known to be 2EXPTIME-complete under the proviso of unary encoding of numbers in cardinality constraints. We show that this assumption can be dropped without an increase in complexity and EXPTIME-completeness can be achieved when bounding the number of query atoms, using a novel reduction from query entailment to knowledge base satisfiability. These findings allow to strengthen other results regarding query entailment and query containment problems in very expressive description logics. Our results also carry over to GC2, the two-variable guarded fragment of first-order logic with counting quantifiers, for which hitherto only conjunctive query entailment has been investigated.

scholarly journals Finite Controllability for Ontology-Mediated Query Answering of CRPQ

2020 ◽  
Author(s):  
Diego Figueira ◽  
Santiago Figueira ◽  
Edwin Pin Baque
Keyword(s):  
Query Answering ◽  
Graph Structure ◽  
First Order ◽  
Underlying Graph ◽  
Graph Classes ◽  
Regular Path ◽  
Order Constraints ◽  
Simple Recursion ◽  
Regular Path Queries ◽  
Path Queries

Finite ontology mediated query answering (FOMQA) is the variant of ontology mediated query answering (OMQA) where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We study the property of finite-controllability, that is, whether FOMQA and OMQA are equivalent, for fragments of C2RPQ. C2RPQ is the language of conjunctive two-way regular path queries, which can be regarded as the result of adding simple recursion to Conjunctive Queries. For graph classes S, we consider fragments C2RPQ(S) of C2RPQ as the queries whose underlying graph structure is in S. We completely classify the finitely controllable and non-finitely controllable fragments under: inclusion dependencies, (frontier-)guarded rules, frontier-one rules (either with or without constants), and more generally under guarded-negation first-order constraints. For the finitely controllable fragments, we show a reduction to the satisfiability problem for guarded-negation first-order logic, yielding a 2EXPTIME algorithm (in combined complexity) for the corresponding (F)OMQA problem.

scholarly journals Regular Path Queries in Lightweight Description Logics: Complexity and Algorithms

2015 ◽  
Vol 53 ◽  
pp. 315-374 ◽  
Author(s):  
Meghyn Bienvenu ◽  
Magdalena Ortiz ◽  
Mantas Simkus
Keyword(s):  
Description Logic ◽  
Query Language ◽  
Description Logics ◽  
Knowledge Bases ◽  
Query Answering ◽  
Complexity Bounds ◽  
Regular Path ◽  
Regular Path Queries ◽  
Path Navigation ◽  
Path Queries

Conjunctive regular path queries are an expressive extension of the well-known class of conjunctive queries. Such queries have been extensively studied in the (graph) database community, since they support a controlled form of recursion and enable sophisticated path navigation. Somewhat surprisingly, there has been little work aimed at using such queries in the context of description logic (DL) knowledge bases, particularly for the lightweight DLs that are considered best suited for data-intensive applications. This paper aims to bridge this gap by providing algorithms and tight complexity bounds for answering two-way conjunctive regular path queries over DL knowledge bases formulated in lightweight DLs of the DL-Lite and EL families. Our results demonstrate that in data complexity, the cost of moving to this richer query language is as low as one could wish for: the problem is NL-complete for DL-Lite and P-complete for EL. The combined complexity of query answering increases from NP- to PSpace-complete, but for two-way regular path queries (without conjunction), we show that query answering is tractable even with respect to combined complexity. Our results reveal two-way conjunctive regular path queries as a promising language for querying data enriched by ontologies formulated in DLs of the DL-Lite and EL families or the corresponding OWL 2 QL and EL profiles.

PAIRPQ: An Efficient Path Index for Regular Path Queries on Knowledge Graphs

2021 ◽  
pp. 106-120
Author(s):  
Baozhu Liu ◽  
Xin Wang ◽  
Pengkai Liu ◽  
Sizhuo Li ◽  
Xiaofei Wang
Keyword(s):  
Path Index ◽  
Regular Path ◽  
Regular Path Queries ◽  
Knowledge Graphs ◽  
Path Queries

Logics for the Semantic Web

2011 ◽  
pp. 24-43
Author(s):  
J. Bruijn
Keyword(s):  
Semantic Web ◽  
Logic Programming ◽  
Description Logic ◽  
Description Logics ◽  
Order Logic ◽  
First Order Logic ◽  
Horn Logic ◽  
First Order ◽  
Logical Language ◽  
Rule Languages

This chapter introduces a number of formal logical languages which form the backbone of the Semantic Web. They are used for the representation of both ontologies and rules. The basis for all languages presented in this chapter is the classical first-order logic. Description logics is a family of languages which represent subsets of first-order logic. Expressive description logic languages form the basis for popular ontology languages on the Semantic Web. Logic programming is based on a subset of first-order logic, namely Horn logic, but uses a slightly different semantics and can be extended with non-monotonic negation. Many Semantic Web reasoners are based on logic programming principles and rule languages for the Semantic Web based on logic programming are an ongoing discussion. Frame Logic allows object-oriented style (frame-based) modeling in a logical language. RuleML is an XML-based syntax consisting of different sublanguages for the exchange of specifications in different logical languages over the Web.

scholarly journals Algebraic rewritings for optimizing regular path queries

2003 ◽  
Vol 296 (3) ◽  
pp. 453-471 ◽  
Author(s):  
Gösta Grahne ◽  
Alex Thomo
Keyword(s):  
Regular Path ◽  
Regular Path Queries ◽  
Path Queries
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