Sylviane R. Schwer

On Generalized Delannoy Paths

A Delannoy path is a minimal path with diagonal steps in

Formalizing Calendars with the Category of Ordinals

{\mathbb Z}^2

Temporal Granularity Enlightened by Knowledge

between two arbitrary points. We extend this notion to the n dimensions space

S-arrangements avec répétitions

{\mathbb Z}^n

Pseudo-Permutations I: First Combinatorial and Lattice Properties

and identify such paths with words on a special kind of alphabet: an S-alphabet. We show that the set of all the words corresponding to Delannoy paths going from one point to another is exactly one class in the congruence generated by a Thue system that we exhibit. This Thue system induces a partial order on this set that is isomorphic to the set of ordered partitions of a fixed multiset where the blocks are sets with a natural order relation. Our main result is that this poset is a lattice.

Le treillis des chemins de Delannoy

Starting from the basic notion of chronology, we provide a natural representation of calendars and appropriate tools for manipulating them, inside the framework of finite ordinals category. We show that calendars are closed under infimum and supremum operations but not under direct limits.

Ontologies temporelles et sémantique de la temporalité

The formalization of periods of time inside a linear model of Time are based on the notion of intervals, that can or not contain their endpoints. It is quite insufficient when these periods are expressing in terms of coarse granularities with respect to the event taken into account. For instance, how to express the inter-war period in terms of a years interval? This paper presents a new type of interval and the extension of operations on intervals to this new type, in order to reduce the gap between the discourse related to temporal relationship and its translation into a discretized model of Time in databases.