Publications Scientifiques

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Author: search.filters.author.Chaabani, Mohamed

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Now showing 1 - 6 of 6
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    Verified Path Indexing
    (pringer Science and Business Media Deutschland GmbH, 2025) Chaabani, Mohamed; Robillard, Simon
    The indexing of syntactic terms is a key component for the efficient implementation of automated theorem provers. This paper presents the first verified implementation of a term indexing data structure, namely a formalization of path indexing in the proof assistant Isabelle/HOL. We define the data structure, maintenance operations, and retrieval operations, including retrieval of unifiable terms, instances, generalizations and variants. We prove that maintenance operations preserve the invariants of the structure, and that retrieval operations are sound and complete
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    Formalisation de la logique de description ALC dans l'assistant de preuve Coq
    (2009) Chaabani, Mohamed; Mezghiche, Mohamed; Strecker, Martin
    Le langage d’ontologie Web (Web Ontology Language OWL) est un langage utilis ́e pour le web s ́emantique. OWL est bas ́e sur les logiques de description (LD), une famille de lan- gages adapt ́es pour la repr ́esentation et le raisonnement sur des connaissances d’un domaine d’application d’une fa ̧con structur ́ee et formelle. Le web s ́emantique est actuellement l’un des champs d’application des m ́ethodes formelles, dont l’objectif est d’assurer leur fiabilit ́e. Un point essentiel de l’application de ces m ́ethodes formelles est la preuve de va- lidit ́e des raisonnements dans des LDs, comme celle de la terminaison, l’ad ́equation (soundness) et la compl ́etude d’un raisonneur. Dans ce papier, on pr ́esente une sp ́ecification formelle de la syntaxe et de la s ́emantique de ALC, qui est consid ́er ́ee comme un repr ́esentant typique d’une large gamme de LDs. On prouve pour cette logique les pro- pri ́et ́es d’ad ́equation, de compl ́etude et de terminaison dans l’assistant de preuve Coq.
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    Vérification d'une méthode de preuve pour la logique de description ALC
    (2010) Chaabani, Mohamed; Mezghiche, Mohamed; Strecker, Martin
    Les logiques de description (DLs) sont une famille de langages utilisés pour la représentation et le raisonnement sur des connaissances d’un domaine d’application d’une manière structurée et formelle. Pour atteindre cet objectif, plusieurs raisonneurs ont été implantés, comme RACER et FACT++. Toutes ces implantations n’ont pas encore été certifiées. Pour garantir la correction des déri- vations des propriétés dans les DLs, il s’avère nécessaire de valider formellement le processus de raisonnement appliqué aux DLs. Dans ce papier, nous présentons une définition d’un raisonneur pour la logique de description ALC basé sur la méthode du tableau sémantique. On assure la validité de notre raisonneur par la preuve des propriétés de son adéquation, de sa complétude et de sa terminaison dans l’assistant de preuve Isabelle/HOL. La preuve procède en deux étapes: elle établit les propriétés sur un niveau abstrait, ensembliste, et les instancie ensuite pour une implantation sur des listes.
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    A Formalized procedure for database horizontal fragmentation in isabelle/HOL Proof Assistant
    (Springer, 2018) Cheikh, Salmi; Chaabani, Mohamed; Mezghiche, Mohamed
    We propose a logical procedure for the horizontal fragmentation problem based on predicate abstraction over the entire domain of database relations. The set of minterm predicates is constructed using rewriting rules similar to the well-known semantic tableau algorithm. The procedure start from an initial set of simple predicates, build the set of minterm predicates until rules are no longer required. To ensure this proposition, we give a formal proof of its correctness namely, it’s soundness, completeness and termination with Isabelle proof assistant. The main contribution of this work are: refining the minterm approach by adding a semantic layer to predicates, minimizing the set of minterm predicates by automatically eliminating contradictory ones, detecting and handling subsumptions between them. This leads to the best construction time of the final partitioning schema. Finally, a source code of the procedure is generated automatically by the Isabelle proof assistant.
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    A practical approach for verification of graph transformation with description logic
    (2020) Chaabani, Mohamed; Mezghiche, Mohamed
    Graphs and visual models play a central role in the modeling and meta-modeling of software systems, these models are specified using a modeling formalism, in a high-level abstraction independent of the platform, in which the focus is on the concepts rather than the implementation. This allows keeping the model, transporting it, and then transforming it into code. Several graph transformation tools have been developed to ensure efficient transformations. This transformation requires a process of verification and validation to guarantee the correction of this transformation process, of which there are different ways to checking that a software system achieves its goal. In computer science, formal methods are techniques that allow rigorous reasoning, using semantic and formal methods, to prove their validity with respect to a certain set of properties. In this sense, description logics are promising candidates for encoding graph structures and reasoning about graph transformations, they are privileged target to operationalize graph transformation tools because they have the mechanisms of reasoning or inference
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    Logical foundations for reasoning about transformations of knowledge bases
    (2013) Chaabani, Mohamed; Echahed, R.; Strecker, M.
    This paper is about transformations of knowledge bases with the aid of an imperative programming language which is non-standard in the sense that it features conditions (in loops and selection statements) that are description logic (DL) formulas, and a non-deterministic assignment statement (a choice operator given by a DL formula). We sketch an operational semantics of the proposed programming language and then develop a matching Hoare calculus whose pre- and post-conditions are again DL formulas. A major difficulty resides in showing that the formulas generated when calculating weakest preconditions remain within the chosen DL fragment. In particular, this concerns substitutions whose result is not directly representable. We therefore explicitly add substitution as a constructor of the logic and show how it can be eliminated by an interleaving with the rules of a traditional tableau calculus