An ALC(D)-based combination of temporal constraints and spatial constraints suitable for continuous (spatial) change

TL;DR

This paper introduces a new spatio-temporal logic framework combining ALC(D) with temporal and spatial constraints, enabling reasoning about continuous spatial change and motion in dynamic scenes.

Contribution

It extends ALC(D) by integrating TCSP-based temporal constraints and RCC8-based spatial relations, addressing continuous change in a unified logical setting.

Findings

Framework supports reasoning about continuous spatial change.

Uses a partition of Allen's relations to handle overlapping truths.

Enables modeling of dynamic spatial scenes with durative truths.

Abstract

We present a family of spatio-temporal theories suitable for continuous spatial change in general, and for continuous motion of spatial scenes in particular. The family is obtained by spatio-temporalising the well-known ALC(D) family of Description Logics (DLs) with a concrete domain D, as follows, where TCSPs denotes "Temporal Constraint Satisfaction Problems", a well-known constraint-based framework: (1) temporalisation of the roles, so that they consist of TCSP constraints (specifically, of an adaptation of TCSP constraints to interval variables); and (2) spatialisation of the concrete domain D: the concrete domain is now $D_x$, and is generated by a spatial Relation Algebra (RA) $x$, in the style of the Region-Connection Calculus RCC8. We assume durative truth (i.e., holding during a durative interval). We also assume the homogeneity property (if a truth holds during a given interval, it holds during all of its subintervals). Among other things, these assumptions raise the "conflicting" problem of overlapping truths, which the work solves with the use of a specific partition of the 13 atomic relations of Allen's interval algebra.