Elzbieta Hajnicz

Intervals in non-linear point time.
The longer paper

868

Abstract

This report contains a characterization of time intervals defined in point time framework. We start from presenting brief description of non-linear point time structures. Next basic properties of sets of points and pairs of points are suggested, and their comparison is conducted.

For intervals defined as sets of points, the theories of interval time structures are based on a precedence relation $\prec$ and the inclusion relation $\subseteq$ or the overlapping relation ${\cal O}$, whereas for intervals defined as pairs of points, the first theory is based on the beginning and ending inclusion relations $\subset_B$ and $\subset_E$, whereas the second theory is based on the inclusion relation $\subseteq$ and the precedence relation $\prec$. In the case of sets of points, several theories are presented depending on definition of precedence relation, and for solid intervals as well. Complete axiomatizations are presented for all the theories depending on definition of intervals and relations ordering them.

Key Words : nonlinear time structures, time points, time intervals, set of points, pair of points.