arXiv subjects

Rachid Echahed

Publications and source records attributed to Rachid Echahed.

At least 19 recordsLinked to original sources

arXiv2026

Sketch-Oriented Databases

This paper introduces sketch-oriented databases, a categorical framework that encodes database paradigms as finite-limit sketches and individual databases and schemas as set-valued models. It illustrates the formalism through graph-oriented paradigms such as quivers, RDF triplestores and property graphs. It also shows how common graph features such as labels, attributes, typing, and paths, are uniformly captured by sketch constructions. Because paths play an important role in queries, we propose inference rules formalized via localizers to compute useful paths lazily; such localizers are also useful for tasks like database type conformance. Finally, the paper introduces stuttering sketches, whose aim is to facilitate modular composition and scalable model growth: stuttering sketches are finite-limit sketches in which relations are specified by a single limit instead of two nested limits, and the paper proves that finite unions of models of a stuttering sketch are pointwise colimits.

cs.LO↗

arXiv2026

Repairing Property Graphs under PG-Constraints

Recent standardization efforts for graph databases lead to standard query languages like GQL and SQL/PGQ, and constraint languages like Property Graph Constraints (PG-Constraints). In this paper, we embark on the study of repairing property graphs under PG-Constraints. We identify a significant subset of PG-Constraints, encoding denial constraints and including recursion as a key feature, while still permitting automata-based structural analyses of errors. We present a comprehensive repair pipeline for these constraints to repair Property Graphs, involving changes in the graph topology and leading to node, edge and, optionally, label deletions. We investigate three algorithmic strategies for the repair procedure, based on Integer Linear Programming (ILP), a naive, and an LP-guided greedy algorithm. Our experiments on various real-world datasets reveal that repairing with label deletions can achieve a 59% reduction in deletions compared to node/edge deletions. Moreover, the LP-guided greedy algorithm offers a runtime advantage of up to 97% compared to the ILP strategy, while matching the same quality.

cs.DB↗

arXiv2022

A Rule-based Operational Semantics of Graph Query Languages

We consider a core language of graph queries. These queries are seen as formulas to be solved with respect to graph-oriented databases. For this purpose, we first define a graph query algebra where some operations over graphs and sets of graph homomorphisms are specified. Then, the notion of pattern is introduced to represent a kind of recursively defined formula over graphs. The syntax and formal semantics of patterns are provided. Afterwards, we propose a new sound and complete calculus to solve patterns. This calculus, which is based on a rewriting system, develops only one derivation per pattern to be solved. Our calculus is generic in the sense that it can be adapted to different kinds of graph databases provided that the notions of graph and graph homomorphism (match) are well defined.

cs.LO↗

arXiv2021

Querying RDF Databases with Sub-CONSTRUCTs

Graph query languages feature mainly two kinds of queries when applied to a graph database: those inspired by relational databases which return tables such as SELECT queries and those which return graphs such as CONSTRUCT queries in SPARQL. The latter are object of study in the present paper. For this purpose, a core graph query language GrAL is defined with focus on CONSTRUCT queries. Queries in GrAL form the final step of a recursive process involving so-called GrAL patterns. By evaluating a query over a graph one gets a graph, while by evaluating a pattern over a graph one gets a set of matches which involves both a graph and a table. CONSTRUCT queries are based on CONSTRUCT patterns, and sub-CONSTRUCT patterns come for free from the recursive definition of patterns. The semantics of GrAL is based on RDF graphs with a slight modification which consists in accepting isolated nodes. Such an extension of RDF graphs eases the definition of the evaluation semantics, which is mainly captured by a unique operation called Merge. Besides, we define aggregations as part of GrAL expressions, which leads to an original local processing of aggregations.

cs.DB↗

arXiv2021

A Superposition-Based Calculus for Quantum Diagrammatic Reasoning and Beyond

We introduce a class of rooted graphs which allows one to encode various kinds of classical or quantum circuits. We then follow a set-theoretic approach to define rewrite systems over the considered graphs and propose a new complete Superposition callculus which handles sets of formulas consisting of equations or disequations over these graphs.

cs.LO↗

arXiv2020

An Algebraic Graph Transformation Approach for RDF and SPARQL

We consider the recommendations of the World Wide Web Consortium (W3C) about RDF framework and its associated query language SPARQL. We propose a new formal framework based on category theory which provides clear and concise formal definitions of the main basic features of RDF and SPARQL. We define RDF graphs as well as SPARQL basic graph patterns as objects of some nested categories. This allows one to clarify, in particular, the role of blank nodes. Furthermore, we consider basic SPARQL CONSTRUCT and SELECT queries and formalize their operational semantics following a novel algebraic graph transformation approach called POIM.

cs.DB↗

arXiv2020

All You Need Is CONSTRUCT

In SPARQL, the query forms SELECT and CONSTRUCT have been the subject of several studies, both theoretical and practical. However, the composition of such queries and their interweaving when forming involved nested queries has not yet received much interest in the literature. We mainly tackle the problem of composing such queries. For this purpose, we introduce a language close to SPARQL where queries can be nested at will, involving either CONSTRUCT or SELECT query forms and provide a formal semantics for it. This semantics is based on a uniform interpretation of queries. This uniformity is due to an extension of the notion of RDF graphs to include isolated items such as variables. As a key feature of this work, we show how classical SELECT queries can be easily encoded as a particular case of CONSTRUCT queries.

cs.DB↗

arXiv2020

On foundational aspects of RDF and SPARQL

We consider the recommendations of the World Wide Web Consortium (W3C) about the Resource Description Framework (RDF) and the associated query language SPARQL. We propose a new formal framework based on category theory which provides clear and concise formal definitions of the main basic features of RDF and SPARQL. We propose to define the notions of RDF graphs as well as SPARQL basic graph patterns as objects of some nested categories. This allows one to clarify, in particular, the role of blank nodes. Furthermore, we consider basic SPARQL CONSTRUCT and SELECT queries and formalize their operational semantics following a novel algebraic graph transformation approach called POIM.

cs.DB↗

arXiv2019

Proceedings Tenth International Workshop on Graph Computation Models

This volume contains the post-proceedings of the Tenth International Workshop on Graph Computation Models (GCM 2019: http://gcm2019.imag.fr). The workshop was held in Eindhoven, The Netherlands, on July 17th, 2019, as part of STAF 2019 (Software Technologies: Applications and Foundations). Graphs are common mathematical structures that are visual and intuitive. They constitute a natural and seamless way for system modelling in science, engineering and beyond, including computer science, biology, business process modelling, etc. Graph computation models constitute a class of very high-level models where graphs are first-class citizens. The aim of the International GCM Workshop series is to bring together researchers interested in all aspects of computation models based on graphs and graph transformation. It promotes the cross-fertilizing exchange of ideas and experiences among senior and young researchers from the different communities interested in the foundations, applications, and implementations of graph computation models and related areas. These post-proceedings contain four selected papers from GCM2019 proceedings and an invited presentation that gives an account of the very successful panel discussion dedicated to the Analysis of Graph Transformation Systems, which took place during the workshop and was animated by Reiko Heckel, Leen Lambers and Maryam Ghaffari Saadat. All submissions were subject to careful refereeing. The topics of accepted papers include theoretical aspects of graph transformation and parsing techniques as well as an application to model-driven engineering.

cs.LO↗

arXiv2019

True Parallel Graph Transformations: an Algebraic Approach Based on Weak Spans

We address the problem of defining graph transformations by the simultaneous application of direct transformations even when these cannot be applied independently of each other. An algebraic approach is adopted, with production rules of the form $L\xleftarrow{l}K \xleftarrow{i} I \xrightarrow{r} R$, called weak spans. A parallel coherent transformation is introduced and shown to be a conservative extension of the interleaving semantics of parallel independent direct transformations. A categorical construction of finitely attributed structures is proposed, in which parallel coherent transformations can be built in a natural way. These notions are introduced and illustrated on detailed examples.

cs.LO↗

arXiv2018

A Set-Theoretic Framework for Parallel Graph Rewriting

We tackle the problem of attributed graph transformations and propose a new algorithmic approach for defining parallel graph transformations allowing overlaps. We start by introducing some abstract operations over graph structures. Then, we define the notion of rewrite rules as three inclusions of the form $L \supseteq K \supseteq M \subseteq R$. We provide six conditions that parallel graph rewrite relations should ideally satisfy, which lead us to define two distinct full parallel graph rewrite relations. A central notion of regularity of matchings is proved to be equivalent to these six conditions, and to the equality of these two relations. Furthermore, we take advantage of the symmetries that may occur in $L$, $K$, $M$ and $R$ and define another pair of rewrite relations that factor out possibly many equivalent matchings up to their common symmetries. These definitions and the corresponding proofs combine operations on graphs with group-theoretic notions, thus illustrating the relevance of our framework.

cs.LO↗

arXiv2018

On the Verification of Logically Decorated Graph Transformations

We address the problem of reasoning on graph transformations featuring actions such as \emph{addition} and \emph{deletion} of nodes and edges, node \emph{merging} and \emph{cloning}, node or edge \emph{labelling} and edge \emph{redirection}. First, we introduce the considered graph rewrite systems which are parameterized by a given logic $\mathcal{L}$. Formulas of $\mathcal{L}$ are used to label graph nodes and edges. In a second step, we tackle the problem of formal verification of the considered rewrite systems by using a Hoare-like weakest precondition calculus. It acts on triples of the form $\{\texttt{Pre}\}(\texttt{R},\texttt{strategy}) \{\texttt{Post}\}$ where \texttt{Pre} and \texttt{Post} are conditions specified in the given logic $\mathcal{L}$, \texttt{R} is a graph rewrite system and \texttt{strategy} is an expression stating how rules in \texttt{R} are to be performed. We prove that the calculus we introduce is sound. Moreover, we show how the proposed framework can be instantiated successfully with different logics. We investigate first-order logic and several of its decidable fragments with a particular focus on different dialects of description logic (DL). We also show, by using bisimulation relations, that some DL fragments cannot be used due to their lack of expressive power.

cs.LO↗

arXiv2017

Parallel Graph Rewriting with Overlapping Rules

We tackle the problem of simultaneous transformations of networks represented as graphs. Roughly speaking, one may distinguish two kinds of simultaneous or parallel rewrite relations over complex structures such as graphs: (i) those which transform disjoint subgraphs in parallel and hence can be simulated by successive mere sequential and local transformations and (ii) those which transform overlapping subgraphs simultaneously. In the latter situations, parallel transformations cannot be simulated in general by means of successive local rewrite steps. We investigate this last problem in the framework of overlapping graph transformation systems. As parallel transformation of a graph does not produce a graph in general, we propose first some sufficient conditions that ensure the closure of graphs by parallel rewrite relations. Then we mainly introduce and discuss two parallel rewrite relations over graphs. One relation is functional and thus deterministic, the other one is not functional for which we propose sufficient conditions which ensure its confluence.

cs.FL↗

arXiv2015

AGREE -- Algebraic Graph Rewriting with Controlled Embedding (Long Version)

The several algebraic approaches to graph transformation proposed in the literature all ensure that if an item is preserved by a rule, so are its connections with the context graph where it is embedded. But there are applications in which it is desirable, for example when cloning an item, to specify different embeddings for the original and for the copy. Therefore we propose a conservative extension of these approaches where a rule can specify how the embedding of a preserved item should be changed, typically by removing certain connections.

cs.LO↗

arXiv2014

SROIQsigma is decidable

We consider a dynamic extension of the description logic $\mathcal{SROIQ}$. This means that interpretations could evolve thanks to some actions such as addition and/or deletion of an element (respectively, a pair of elements) of a concept (respectively, of a role). The obtained logic is called $\mathcal{SROIQ}$ with explicit substitutions and is written $\mathcal{SROIQ^σ}$. Substitution is not treated as meta-operation that is carried out immediately, but the operation of substitution may be delayed, so that sub-formulae of $\mathcal{SROIQ}^σ$ are of the form $Φσ$, where $Φ$ is a $\mathcal{SROIQ}$ formula and $σ$ is a substitution which encodes changes of concepts and roles. In this paper, we particularly prove that the satisfiability problem of $\mathcal{SROIQ}^σ$ is decidable.

cs.LO↗

arXiv2014

Transformation of Attributed Structures with Cloning (Long Version)

Copying, or cloning, is a basic operation used in the specification of many applications in computer science. However, when dealing with complex structures, like graphs, cloning is not a straightforward operation since a copy of a single vertex may involve (implicitly)copying many edges. Therefore, most graph transformation approaches forbid the possibility of cloning. We tackle this problem by providing a framework for graph transformations with cloning. We use attributed graphs and allow rules to change attributes. These two features (cloning/changing attributes) together give rise to a powerful formal specification approach. In order to handle different kinds of graphs and attributes, we first define the notion of attributed structures in an abstract way. Then we generalise the sesqui-pushout approach of graph transformation in the proposed general framework and give appropriate conditions under which attributed structures can be transformed. Finally, we instantiate our general framework with different examples, showing that many structures can be handled and that the proposed framework allows one to specify complex operations in a natural way.

cs.SE↗

arXiv2013

Proceedings 7th International Workshop on Computing with Terms and Graphs

This volume contains the proceedings of the Seventh International Workshop on Computing with Terms and Graphs (TERMGRAPH 2013). The workshop took place in Rome, Italy, on March 23rd, 2013, as part of the sixteenth edition of the European Joint Conferences on Theory and Practice of Software (ETAPS 2013). Research in term and graph rewriting ranges from theoretical questions to practical issues. Computing with graphs handles the sharing of common subexpressions in a natural and seamless way, and improves the efficiency of computations in space and time. Sharing is ubiquitous in several research areas, as witnessed by the modelling of first- and higher-order term rewriting by (acyclic or cyclic) graph rewriting, the modelling of biological or chemical abstract machines, and the implementation techniques of programming languages: many implementations of functional, logic, object-oriented, concurrent and mobile calculi are based on term graphs. Term graphs are also used in automated theorem proving and symbolic computation systems working on shared structures. The aim of this workshop is to bring together researchers working in different domains on term and graph transformation and to foster their interaction, to provide a forum for presenting new ideas and work in progress, and to enable newcomers to learn about current activities in term graph rewriting. These proceedings contain six accepted papers and the abstracts of two invited talks. All submissions were subject to careful refereeing. The topics of accepted papers range over a wide spectrum, including theoretical aspects of term graph rewriting, concurrency, semantics as well as application issues of term graph transformation.

cs.SC↗

arXiv2012

Graph rewriting with polarized cloning

We tackle the problem of graph transformation with a particular focus on node cloning. We propose a new approach to graph rewriting where nodes can be cloned zero, one or more times. A node can be cloned together with all its incident edges, with only its outgoing edges, with only its incoming edges or with none of its incident edges. We thus subsume previous works such as the sesqui-pushout, the heterogeneous pushout and the adaptive star grammars approaches. A rewrite rule is defined as a span where the right-hand and left-hand sides are graphs while the interface is a polarized graph. A polarized graph is a graph endowed with some annotations on nodes. The way a node is cloned is indicated by its polarization annotation. We use these annotations for designing graph transformation with polarized cloning. We show how a clone of a node can be built according to the different possible polarizations and define a rewrite step as a final pullback complement followed by a pushout. This is called the polarized sesqui-pushout approach. We also provide an algorithmic presentation of the proposed graph transformation with polarized cloning.

cs.LO↗