On the utilization of spatial structures for cognitively plausible and efficient reasoning

Tripartite Line Tracks – Bipartite Line Tracks

“…every position is possible BLT (2-3-4-5) BLT (1)(2)(3)(4)(5)(6) BLT (1-6) BLT (3)(4) We assume that one is able to retain coarsely the vector a → b after b has been occluded, at least for a short moment. Thus, when realising c, it can be described with respect to a → b, and this relationship is easier to keep in mind than the single position of b, which gradually diminishes.…”

“…Among other reasoning tasks, [5] considered the problem of specifying a short cut from a position a to another position c, given the position of c with respect to the path a → b. More formally, the idea is to deduce a position b relative to a vector a → c, provided that position c with respect to the vector a → b is known.…”

“…This concerns particularly navigation tasks where the position of objects are described with respect to landmarks. One example is a simple localisation task, stated by [5]:…”

“…Our description will be restricted to two-dimensional polygonal outlines since we are mainly interested in demonstrating how shape descriptions can be devised by considering orientation information and navigation tasks. For that purpose, we will confine ourselves to one single approach from Freksa and Zimmermann which is described in [5], and which we will adopt to shape reasoning problems. …”

Reasoning about intervals in two dimensions

“…In contrast to these generalisations, which are based on point configurations ( [7], [13]), regions ([3], [4]), or orthogonal projections of twodimensional objects on a number of different axes ( [10], [11]), our new representation is based on intervals which are embedded in the two-dimensional plane. A few approaches deal with linear entities in two dimensions: line-line relations are found in [5] but these concern arbitrarily curved lines rather than straight intervals.…”