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. © 2012 IEEE.

An Integrated first-order theory of points and intervals: Expressive power in the class of all linear orders

SCIAVICCO, Guido
2012

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. © 2012 IEEE.
2012
9780769548029
Definability; First-order logic; Interval; Point and mixed relations;
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2326767
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