A qualitative spatial representation of string loops as holes

This research note contains an extension of a previous work by Cabalar and Santos (2011) that formalised several spatial puzzles formed by strings and holes. That approach explicitly ignored some configurations and actions that were irrelevant for the studied puzzles but are physically possible and may become crucial for other spatial reasoning problems. In particular, the previous work did not consider the formation of string loops or the situations where a holed object is partially crossed by another holed object. In this paper, we remove these limitations by treating string loops as dynamic holes that can be created or destroyed by a pair of elementary actions, respectively picking or pulling from strings. We explain how string loops can be recognised in a data structure representing the domain states and define a notation to represent crossings through string loops. The resulting formalism is dual in the sense that it also allows understanding any hole as a kind of (sometimes rigid) closed string loop.