Abstract
There are two natural and well-studied approaches
to temporal ontology and reasoning, that is, pointbased
and interval-based. Usually, interval-based temporal
reasoning deals with points as a particular case of duration-less
intervals. Recently, a two-sorted point-interval temporal logic
in a modal framework in which time instants (points) and time
periods (intervals) are considered on a par has been presented.
We consider here two-sorted first-order languages, interpreted
in the class of all linear orders, based on the same principle,
with relations between points, between intervals, and intersort.
First, for those languages containing only interval-interval,
and only inter-sort relations we give complete classifications
of their sub-fragments in terms of relative expressive power,
determining how many, and which, are the different two-sorted
first-order languages with one or more such relations. Then,
we consider the full two-sorted first-order logic with all the
above mentioned relations, restricting ourselves to identify all
expressively complete fragments and all maximal expressively
incomplete fragments, and posing the basis for a forthcoming
complete classification.