The set of closed intervals of ℝ is provided with a semigroup structure. We complete this semigroup to obtain a 2-dimensional vector space. But neither associative nor nonassociative algebra structure ...

Abstract: Interval algebra networks are traditionally defined over finite intervals. In this paper, we relax this restriction by allowing one or more of the intervals involved to be infinite. We then ...

A modern C++ header-only library implementing Disjoint Interval Sets as a complete Boolean algebra, featuring an elegant STL-aligned API, compile-time interval arithmetic, and mathematical notation ...

Abstract: In this paper, we propose an ontology-based approach for representing and reasoning about precise and imprecise time intervals. This approach is three folds: (i) extending the 4D-fluents ...

ABSTRACT: This paper introduces the concept and motivates the use of finite-interval based measures for physically realizable and measurable quantities, which we call D-measures. We demonstrate the ...