Seminars

Speaker: Pierre Pradic — perso.ens-lyon.fr/pierre.pradic/

Title: Synthesizing Nested Relational Queries from Implicit Specifications

Abstract:
Derived datasets can be defined implicitly or explicitly. An implicit
definition (of dataset O in terms of datasets I⃗ ) is a logical specification
involving the source data I⃗ and the interface data O. It is a valid definition
of O in terms of I⃗ , if any two models of the specification agreeing on I⃗
agree on O. In contrast, an explicit definition is a query that produces O from
I⃗ . Variants of Beth's theorem state that one can convert implicit definitions
to explicit ones. Further, this conversion can be done effectively given a
proof witnessing implicit definability in a suitable proof system. In this
talk, I will discuss an analogous effective implicit-to-explicit result for
nested relations: implicit definitions, given in the natural logic for nested
relations, can be effectively converted to explicit definitions in the nested
relational calculus NRC.

I will first spend some time explaining what NRC is and what logic we use to
describe implicit definitions of nested queries. Then I will present the
results obtained in our papers, attempt to give some intuitions on the proof of
the main theorem and say a few words on in particular the proof-theoretic
techniques and concerns that come up (namely, cut-elimination and focussing)
and how this can impact the complexity of extracting explicit definitions from
proofs of implicit definability. Then if time allows I will discuss a more
general model-theoretic result that we first used to give a non-constructive
proof of our theorem, and some ideas that we have towards making it
constructive and bounding the complexity of extracting explicit definitions.

This is Joint work with Michael Benedikt and Christoph Wenhard. The main
results I will be discussing were written up in
arxiv.org/abs/2005.06503 and arxiv.org/abs/2209.08299.

Speaker : Luis Galárraga — luisgalarraga.de/about/

Title: Computing How-Provenance for SPARQL Queries via Query Rewriting

Abstract:
Over the past few years, we have witnessed the emergence of large knowledge graphs built by extracting and combining information from multiple sources. This has propelled many advances in query processing over knowledge graphs, however the aspect of providing provenance explanations for query results has so far been mostly neglected. In this talk I will present SPARQLprov, a method based on query rewriting, to compute how-provenance polynomials for SPARQL queries over knowledge graphs. Contrary to existing works, SPARQLprov is system-agnostic and can be applied to standard and already deployed SPARQL engines without the need of customized extensions. To do so, we rely on spm-semirings to compute polynomial annotations that respect the property of commutation with homomorphisms on monotonic and non-monotonic SPARQL queries without aggregate functions. An evaluation on real and synthetic data shows that SPARQLprov over standard engines competes with state-of-the-art solutions for how-provenance computation, while covering a larger fragment of the query language.

Title:The Regular Languages of First-Order Logic with One Alternation
Abstract: The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. Specifically, it is shown that if an arbitrary Σ2 formula defines a regular language with a neutral letter, then there is an equivalent Σ2 formula that only uses the order predicate. This shows that the so-called Central Conjecture of Straubing holds for Σ2 over languages with a neutral letter, the first progress on the Conjecture in more than 20 years. To show the characterization, lower bounds against polynomial-size depth-3 Boolean circuits with constant top fan-in are developed. The heart of the combinatorial argument resides in studying how positions within a language are determined from one another, a technique of independent interest.

Title:
Separator logic, expressive power and algorithmic applications
Abstract:
First-order logic (FO) can express many algorithmic problems on graphs,
but fails to express whether two vertices are connected. We define a
new logic (separator logic) by enriching FO with connectivity
predicates connk(x, y, z1, . . . , zk) that hold true in a graph if
there exists a path between x and y after deletion of z1, . . . , zk.
In this talk I will first present a study of the expressive power of
this new logic.
I will then present algorithmic results for this logic on graph classes
that exclude a topological minor.
These results were obtained in collaboration with Michał Pilipczuk,
Nicole Schirrmacher, Sebastian Siebertz, and Szymon Toruńczyk.

Title: Bornes inférieures superpolynomiales pour les circuits de profondeur constante

Abstract:
Tout polynôme multivarié P(X_1,...,X_n) peut être écrit comme une somme de
monômes, i.e., une somme de produits de variables et de constantes du corps.
La taille naturelle d'une telle expression est le nombre de monômes. Mais,
que se passe-t-il si on rajoute un nouveau niveau de complexité en
considérant les expressions de la forme : somme de produits de sommes (de
variables et de constantes) ? Maintenant, il devient moins clair comment
montrer qu'un polynôme donné n'a pas de petite expression. Dans cet exposé
nous résoudrons exactement ce problème. Plus précisément, nous prouvons que
certains polynômes explicites n'ont pas de représentations "somme de
produits de sommes'' (SPS) de taille polynomiale. Nous pouvons aussi obtenir
des résultats similaires pour les SPSP, SPSPS, etc... pour toutes les
expressions de profondeur constante.
"