Lily Gallois | Université de Lille (original) (raw)

Drafts by Lily Gallois

(An update 7 july )The present contribution delves into a recent development of dialogical rules ... more (An update 7 july )The present contribution delves into a recent development of dialogical rules for proof-theory penned by Ansten Klev that arouse from Per Martin-Löf's take on assertoric knowledge as involved in the notion of valid inference within Constructive Type Theory (CTT). The main aim of our paper is to set out the central steps towards a new Dialogical Framework called Immanent Reasoning II, which on one hand integrates some of the CTT-rules developed by Klev (2023), but on the other it develops further the general tenets of the dialogical perspective on meaning and logic. Different to Klev's approach IR-II contain rules that indicate how to develop plays and winning strategies for a thesis. The paper can also be seen as a case study for combining logical frameworks rather than logics.

Papers by Lily Gallois

Graphs are a framework that is used to represent data of many different applications : transport,... more Graphs are a framework that is used to represent data of many different applications : transport, social network, proteins interaction, open data diffusion and its underlying structure. To manage these graphs, the user needs to express queries to extract data and to express properties to enforce integrity constraints or knowledge/ontology used to represent missing data in the graph. In this PhD thesis, we focus on two different questions : how to evaluate efficiently queries over graph and how to complete graphs to satisfy the properties ? Our approach to optimize the evaluation of queries is to find a query semantically equal to the initial one but easier to evaluate. We focus at a useful subclass of queries : regular path queries. Indeed, path queries are the core of the classical queries over graphs, for example : "which are the cities reachable from each other by an exclusive bus travel ?" In the logical optimisation of queries, one of the core problems is the problem of inclusion of a query into another. This problem is well studied for different classes of queries and paths queries ; however, there are few works that took account integrity constraints satisfied by the graphs. In practice, this could lead to a very efficient optimisation : for the path query x.a + .y and the integrity constraints which impose that the set of edges labelled by a is closed under transitivity, we can prove that under the graphs satisfying this constraints, the queries xa + y and x.a.y are equivalent. One can remark that it is very efficient to answer this query. Our approach is to reduce the inclusion problem where integrity constraints are expressed by word constraints, to a problem of containment of regular languages by using string rewriting systems following the approach introduced by Grahne and Thomo. After proving that this reduction of Grahne and Thomo is partially wrong for finite graphs, we introduce a restriction over the rewriting systems guaranteeing the correctness of this reduction and the decidability of the inclusion. The key idea of our restriction is to bound the number of "parallel steps" for every derivation by a constant. We prove that checking if a system is uniformly-bounded by k is pspace-complete. The second problem is to complete the graph to satisfy the properties. This problem is well studied in the context of relational databases by diverse variants of a same procedure : the chase. Unfortunately, this procedure does create a possibly infinite model and not a finite one as we wish. The classical approach in this context is to check whenever the chase procedure terminates for every instance. However, this question is undecidable in general. Inspired by our uniform-bounded notion for rewriting systems developed in the previous part and a similar notion recently introduced for some chase procedures, we study different definitions of uniform boundedness for different kind of chases and we compare them to each other. Finally, we establish that the notions of uniform boundedness for the chase and the uniform boundedness for string rewriting systems are equivalent for a subclass of word constraints reinforcing the links between reasoning over graphs and reasoning over rewriting systems.

Les graphes sont une maniere de representer les donnees et leur structure sous-jacente utilisee d... more Les graphes sont une maniere de representer les donnees et leur structure sous-jacente utilisee dans differentes applications : transport, reseaux sociaux, interaction de proteines, ... Pour gerer ces graphes, l’utilisateur a besoin d’interroger les donnees du graphe et d’exprimer des proprietes representees par des contraintes satisfaites par le graphe ou des connaissances pour representer les donnees manquantes du graphe. Dans cette these nous nous interessons a deux questions particulieres : comment evaluer efficacement des requetes sur des graphes et comment completer des graphes pour satisfaire les proprietes ? Notre approche d’optimisation d’evaluation des requetes consiste a determiner d’autres requetes semantiquement egales a l’initiale mais plus facile a evaluer, nous portons le soin de cette methode sur les requetes de chemin regulier (RPQ). Ces dernieres sont au coeur des requetes classiques de graphe comme : “quels sont les villes reliees par un trajet uniquement en bus ...

We study the notion of boundedness in the context positive existential rules, that is, wether the... more We study the notion of boundedness in the context positive existential rules, that is, wether there exists an upper bound to the depth of the chase procedure, that is independent from the initial instance. By focussing our attention on the oblivious and the semi-oblivious chase variants, we give a characterization of boundedness in terms of FO-rewritability and chase termination. We show that it is decidable to recognize if a set of rules is bounded for several classes of rules and outline the complexity of the problem.

Talks by Lily Gallois

Conférence donnée au TFJM 2022 de Lille et sur internet le 9 Avril à destination d'élèves du seco... more Conférence donnée au TFJM 2022 de Lille et sur internet le 9 Avril à destination d'élèves du secondaire.

L'objectif principal est de conduire vers des points de vue axiomatique de la Géométrie à travers plusieurs géométries non-euclidiennes.