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

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dc.contributor.author Conradie, Willem
dc.contributor.author Durhan, Salih
dc.contributor.author Sciavicco, Guido
dc.date.accessioned 2012-11-18T19:41:51Z
dc.date.available 2012-11-18T19:41:51Z
dc.date.issued 2012
dc.identifier.citation Conradie, W., Durhany, S. & Sciavicco, G. 2011. An integrated first-order theory of points and intervals : expressive power in the class of all linear orders. TIME 2012: 47-54 en_US
dc.identifier.uri http://hdl.handle.net/10210/8225
dc.description.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. en_US
dc.language.iso en en_US
dc.publisher Willem Conradie , Salih Durhany, and Guido Sciavicco en_US
dc.rights © Willem Conradie , Salih Durhany, and Guido Sciavicco, 2011 en_US
dc.subject First-order logic en_US
dc.subject Point and mixed relations en_US
dc.subject Interval-based temporal reasoning en_US
dc.title An integrated first-order theory of points and intervals : expressive power in the class of all linear orders en_US
dc.type Article en_US

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