There are two natural and well-studied approaches to temporal ontology and
reasoning: point-based and interval-based. Usually, interval-based temporal
reasoning deals with points as a particular case of duration-less intervals. A
recent result by Balbiani, Goranko, and Sciavicco presented an explicit
two-sorted point-interval temporal framework in which time instants (points)
and time periods (intervals) are considered on a par, allowing the perspective
to shift between these within the formal discourse. We consider here two-sorted
first-order languages based on the same principle, and therefore including
relations, as first studied by Reich, among others, between points, between
intervals, and inter-sort. We give complete classifications of its
sub-languages in terms of relative expressive power, thus determining how many,
and which, are the intrinsically different extensions of two-sorted first-order
logic with one or more such relations. This approach roots out the classical
problem of whether or not points should be included in a interval-based
semantics. In this Part II, we deal with the cases of all dense and the case of
all unbounded linearly ordered sets.Comment: This is Part II of the paper `An Integrated First-Order Theory of
Points and Intervals over Linear Orders' arXiv:1805.08425v2. Therefore the
introduction, preliminaries and conclusions of the two papers are the same.
This version implements a few minor corrections and an update to the
affiliation of the second autho
