CONTEJEAN Evelyne
Ph.D
Group : Toccata

Elements for Decidability of Unification modulo Distributivity

Starts on 01/09/1988
Advisor :

Funding :
Affiliation : Université Paris-Saclay
Laboratory :

Defended on 03/04/1992, committee :

Research activities :
   - Automated deduction
   - Rewriting

Abstract :
In this thesis, we give some tools for unification (or equations solving) modulo distributivity (or modulo D) of a symbol f on a symbol g. This theory is one of the last for which it remains still unkown whether it is decidable or not.

In the first part, we study some particular problems obviously decidable, balanced problems containing only some terms without the g symbol. We precisely describe the set of solutions, which is possibly infinite. This is done with structures for which there is a property of unique maximal decomposition with respect to a AC1 operator. In a second part, the notions of indexation and stratification are introduced and are used in order to characterize the equality modulo D of two terms. Then we prove, thanks to stratification, the completeness of a set of transformation rules. This set reduces a problem to a babanced problem, and a balanced problem is solved by AC1 unification on structures. For technical reasons, we only handle a particular sort of problems, caracterized by a condition of acyclicity.

Finally, we describe a new, efficient algorithm for solving systems of linear Diophantine equations.

CAUSAL LEARNING FOR DIAGNOSTIC SUPPORT


CAUSAL UNCERTAINTY QUANTIFICATION UNDER PARTIAL KNOWLEDGE AND LOW DATA REGIMES


MICRO VISUALIZATIONS: DESIGN AND ANALYSIS OF VISUALIZATIONS FOR SMALL DISPLAY SPACES
The topic of this habilitation is the study of very small data visualizations, micro visualizations, in display contexts that can only dedicate minimal rendering space for data representations. For several years, together with my collaborators, I have been studying human perception, interaction, and analysis with micro visualizations in multiple contexts. In this document I bring together three of my research streams related to micro visualizations: data glyphs, where my joint research focused on studying the perception of small-multiple micro visualizations, word-scale visualizations, where my joint research focused on small visualizations embedded in text-documents, and small mobile data visualizations for smartwatches or fitness trackers. I consider these types of small visualizations together under the umbrella term ``micro visualizations.'' Micro visualizations are useful in multiple visualization contexts and I have been working towards a better understanding of the complexities involved in designing and using micro visualizations. Here, I define the term micro visualization, summarize my own and other past research and design guidelines and outline several design spaces for different types of micro visualizations based on some of the work I was involved in since my PhD.