Debasis Mitra, Jackson State University, USA; Gerard Ligozat, Universite Paris-Sud, France; Lail Hossain, Jackson State University, USA
Most of the approaches in the spatio-temporal reasoning area use a relational algebraic framework where the domains of variables are typically not given an explicit considerations ill favor of tile relational constraints between those variables. However, some recent works have shown tile deficiency of those apircoaches in finding a globally consistent solution. For example, in cyclic time-interval problems even path-consistent singleton models are not globally consistent. In this article, we have developed a domain-theoretic approach, which is routinely deployed in the traditional discrete-domain constraint satisfaction problems (CSP), for point-based relations in multi-dimensional Cartesian-space. Our algorithms are also developed for the insertion problem (insert an object in a set of existing ones), which is at the core of any incremental approach for checking global consistolcy (Mitra, 2001). The results might be useful in a real-life modeling activities in any relevant area (e.g., visualization or data-medeling).