Papers by Catherine Dubois
Defining a theory, such as arithmetic, geometry, or set theory, in predicate logic just requires ... more Defining a theory, such as arithmetic, geometry, or set theory, in predicate logic just requires to chose function and predicate symbols and axioms, that express the meaning of these symbols. Using, this way, a single logical framework, to define all these theories, has many advantages. First, it requires less efforts, as the logical connectives, ∧, ∨, ∀... and their associated deduction rules are defined once and for all, in the framework and need not be redefined for each theory. Similarly, the notions of proof, model... are defined once and for all. And general theorems, such as the soundness and the completeness theorems, can be proved once and for all. Another advantage of using such a logical framework is that this induces a partial order between theories. For instance, Zermelo-Fraenkel set theory with the axiom of choice (ZFC) is an extension of Zermelo-Fraenkel set theory (ZF), as it contains the same axioms, plus the axiom of choice. It is thus obvious that any theorem of Z...
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The Foc project develops a formal language to implement certified components called collections. ... more The Foc project develops a formal language to implement certified components called collections. These collections are specied and implemented step by step: the programmer describes formally the properties of the algorithms, the context in which they are executed, the data representation and proves formally that the implemented algorithms satises the specified properties. This programming paradigm implies the use of classic oriented-object features and the use of module features like interfaces and encapsulation of data representation. In this paper we formalize a kernel of the Foc language whose main ingredients are multiple inheritance, late binding, overriding, interfaces and encapsulation of the data representation. We specify formally the semantics, the type system, the soundness of the typing discipline.
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L'atelier AFADL rassemble de nombreux acteurs academiques et industriels interesses par la mi... more L'atelier AFADL rassemble de nombreux acteurs academiques et industriels interesses par la mise en oeuvre de techniques formelles aux divers stades du developpement des logiciels et/ou des systemes. Les articles contenus dans les actes d'AFADL 2014 couvrent un large eventail de techniques, methodes et applications. 6 articles longs et 6 articles courts presentent des resultats nouveaux. Un des articles presente un projet ANR. Enfin 7 articles sont des resumes d'articles deja presentes dans des conferences internationales.
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Dans le but de formaliser des specifications d’exigence ecrites en langage naturel, nous avons ch... more Dans le but de formaliser des specifications d’exigence ecrites en langage naturel, nous avons choisi de modeliser les connaissances du domaine par une ontologie et de representer formellement les specifications par son peuplement. L’approche de peuplement est centree sur l’identification d’instances de proprietes a partir des textes. Pour cela, des regles d’extraction sont acquises automatiquement a partir d’un corpus d’apprentissage, puis appliquees sur les textes pour l’identification de mentions d’instances de propriete representees par des triplets. Ces regles exploitent les niveaux d’analyse lexicale, syntaxique et semantique et sont engendrees a partir des chemins syntaxiques recurrents entre les termes pouvant denoter des instances de concept ou de propriete. Nous mon- trons que l’identification d’instances de pro- prietes permet d’identifier de facon precise les instances de concepts enoncees de facon explicite ou implicite dans les textes.
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arXiv (Cornell University), Jul 8, 2023
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Le Centre pour la Communication Scientifique Directe - HAL - Université Paris Descartes, Jan 30, 2019
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Formal Methods Teaching, 2019
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The language {log} is a Constraint Logic Programming language that natively supports finite sets ... more The language {log} is a Constraint Logic Programming language that natively supports finite sets and constraints such as (non) equality and (non) membership. The set constraints resolution process is mathematically formalised by Dovier et al in [5] using rewriting rules. In this paper we present a formalisation in the Coq proof assistant of the term and constraint algebra, the rewriting rules and check all the examples given in the reference paper by applying the rewriting rules manually with the help of some tailored tactics. The main problem we encountered is the non-determinism captured by the rewriting rules, which prevents us from automating their application in Coq. However the rules for nonmembership and set checking are deterministic. So we propose a function that iteratively applies the latter rules. We prove its correctness with respect to the corresponding rewriting rules. This work is a first step of a larger project whose objective is to provide a formally verified reso...
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Electronic Proceedings in Theoretical Computer Science, 2017
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Lecture Notes in Computer Science, 2016
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Revue d'intelligence artificielle, 2015
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Lecture Notes in Computer Science
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Lecture Notes in Computer Science, 2012
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2013 IEEE 25th International Conference on Tools with Artificial Intelligence, 2013
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Lecture Notes in Computer Science, 2014
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2011 10th Mexican International Conference on Artificial Intelligence, 2011
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Automated Reasoning, 2012
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Papers by Catherine Dubois