Spatial Reasoning about String Loops and Holes in Temporal ASP

This paper introduces a new formalism for the automated solution of spatial scenarios involving strings and holed objects. In particular, we revisit a previous formalisation that allows string loops to be treated as holes, but make a substantial modification by removing a previous limitation that prevented a string to cross its own loops. The formalisation introduced in the present paper relies on string segments as basic entities and achieves a greater degree of elaboration tolerance by using inertia to describe those parts of the physical scenario that are unaffected by a given action. As a representation language, we have used Temporal Answer Set Programming since it provides a simple and natural way to deal with time and inertia while, at the same time, it is accompanied by the automated tool 'telingo' that allows a systematic testing of the effects of any sequence of actions. As an illustrative example, we have studied the African Ring puzzle, a problem involving loops crossed by a unique string, and provided the first formalisation of its solution, to the best of our knowledge.