Willem Conradie ; Salih Durhan ; Guido Sciavicco - An Integrated First-Order Theory of Points and Intervals over Linear Orders (Part II)

lmcs:4832 - Logical Methods in Computer Science, April 1, 2020, Volume 16, Issue 2 - https://doi.org/10.23638/LMCS-16(2:1)2020
An Integrated First-Order Theory of Points and Intervals over Linear Orders (Part II)

Authors: Willem Conradie ; Salih Durhan ; Guido Sciavicco

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.

Volume: Volume 16, Issue 2
Section: Logic for knowledge representation
Published on: April 1, 2020
Accepted on: April 2, 2020
Submitted on: September 17, 2018
Keywords: Computer Science - Logic in Computer Science,03B44,F.4.1,I.2.4


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