scholarly journals Bisimulations on Data Graphs

2018 ◽  
Vol 61 ◽  
pp. 171-213 ◽  
Author(s):  
Sergio Abriola ◽  
Pablo Barceló ◽  
Diego Figueira ◽  
Santiago Figueira
Keyword(s):  
Constraint Satisfaction ◽  
Transitive Closure ◽  
Modal Logics ◽  
Closure Operators ◽  
External Observer ◽  
Complexity Bounds ◽  
Fundamental Notion ◽  
Labeled Graphs ◽  
Non Locality

Bisimulation provides structural conditions to characterize indistinguishability from an external observer between nodes on labeled graphs. It is a fundamental notion used in many areas, such as verification, graph-structured databases, and constraint satisfaction. However, several current applications use graphs where nodes also contain data (the so called "data graphs"), and where observers can test for equality or inequality of data values (e.g., asking the attribute 'name' of a node to be different from that of all its neighbors). The present work constitutes a first investigation of "data aware" bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational indistinguishability for XPath ---a language that extends modal logics like PDL with tests for data equality--- with and without transitive closure operators. We show that in general the problem is PSpace-complete, but identify several restrictions that yield better complexity bounds (coNP, PTime) by controlling suitable parameters of the problem, namely the amount of non-locality allowed, and the class of models considered (graphs, DAGs, trees). In particular, this analysis yields a hierarchy of tractable fragments.

Modal Logics with Transitive Closure

2014 ◽  
pp. 157-189
Author(s):  
Olivier Gasquet ◽  
Andreas Herzig ◽  
Bilal Said ◽  
François Schwarzentruber
Keyword(s):  
Transitive Closure ◽  
Modal Logics

scholarly journals Satisfaction and Implication of Integrity Constraints in Ontology-based Data Access

2019 ◽  
Author(s):  
Charalampos Nikolaou ◽  
Bernardo Cuenca Grau ◽  
Egor V. Kostylev ◽  
Mark Kaminski ◽  
Ian Horrocks
Keyword(s):  
Constraint Satisfaction ◽  
Data Access ◽  
Integrity Constraints ◽  
Functional Dependencies ◽  
Complexity Bounds ◽  
Decidability And Complexity

We extend ontology-based data access with integrity constraints over both the source and target schemas. The relevant reasoning problems in this setting are constraint satisfaction—to check whether a database satisfies the target constraints given the mappings and the ontology—and source-to-target (resp., target-to-source) constraint implication, which is to check whether a target constraint (resp., a source constraint) is satisfied by each database satisfying the source constraints (resp., the target constraints). We establish decidability and complexity bounds for all these problems in the case where ontologies are expressed in DL-LiteR and constraints range from functional dependencies to disjunctive tuple-generating dependencies.

scholarly journals Minimizing Cost Travel in Multimodal Transport Using Advanced Relation Transitive Closure

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Rachid Oucheikh ◽  
Ismail Berrada ◽  
Lahcen Omari
Keyword(s):  
Binary Relation ◽  
Constraint Satisfaction ◽  
Operations Research ◽  
Transitive Closure ◽  
Constraint Satisfaction Problem ◽  
Cost Optimization ◽  
Binary Relations ◽  
Mathematical Background ◽  
Multimodal Transport ◽  
Binary Constraint

The optimization computation is an essential transversal branch of operations research which is primordial in many technical fields: transport, finance, networks, energy, learning, etc. In fact, it aims to minimize the resource consumption and maximize the generated profits. This work provides a new method for cost optimization which can be applied either on path optimization for graphs or on binary constraint reduction for Constraint Satisfaction Problem (CSP). It is about the computing of the “transitive closure of a given binary relation with respect to a property.” Thus, this paper introduces the mathematical background for the transitive closure of binary relations. Then, it gives the algorithms for computing the closure of a binary relation according to another one. The elaborated algorithms are shown to be polynomial. Since this technique is of great interest, we show its applications in some important industrial fields.

scholarly journals Data Complexity and Rewritability of Ontology-Mediated Queries in Metric Temporal Logic under the Event-Based Semantics

2019 ◽  
Author(s):  
Vladislav Ryzhikov ◽  
Przemyslaw Andrzej Walega ◽  
Michael Zakharyaschev
Keyword(s):  
Temporal Logic ◽  
Transitive Closure ◽  
Order Logic ◽  
Data Complexity ◽  
Complexity Bounds ◽  
Metric Temporal Logic ◽  
First Order ◽  
Primitive Recursion ◽  
Lower Complexity ◽  
Event Based

We investigate the data complexity of answering queries mediated by metric temporal logic ontologies under the event-based semantics assuming that data instances are finite timed words timestamped with binary fractions. We identify classes of ontology-mediated queries answering which can be done in AC0, NC1, L, NL, P, and coNP for data complexity, provide their rewritings to first-order logic and its extensions with primitive recursion, transitive closure or datalog, and establish lower complexity bounds.

scholarly journals From Conjunctive Queries to Instance Queries in Ontology-Mediated Querying

2018 ◽  
Author(s):  
Cristina Feier ◽  
Carsten Lutz ◽  
Frank Wolter
Keyword(s):  
Constraint Satisfaction ◽  
Related Problem ◽  
Constraint Satisfaction Problem ◽  
Description Logics ◽  
Complexity Bound ◽  
Conjunctive Queries ◽  
Complexity Bounds

We consider ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and (unions) of conjunctive queries, studying the rewritability into OMQs based on instance queries (IQs). Our results include exact characterizations of when such a rewriting is possible and tight complexity bounds for deciding rewritability. We also give a tight complexity bound for the related problem of deciding whether a given MMSNP sentence (in other words: the complement of a monadic disjunctive Datalog program) is equivalent to a constraint satisfaction problem.

Modal logics with Belnapian truth values

2010 ◽  
Vol 20 (3) ◽  
pp. 279-304 ◽  
Author(s):  
Serge P Odintsov ◽  
Heinrich Wansing
Keyword(s):  
Modal Logics ◽  
Truth Values
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