Holes, Knots and Shapes: A Spatial Ontology of a Puzzle

Logical Formalizations of Commonsense Reasoning

Volume

Papers from the 2007 AAAI Spring Symposium

Contents

In this paper we propose a spatial ontology for reasoning about holes, rigid objects and strings, taking a classical puzzle as a motivating example. In this ontology the domain is composed of spatial regions whereby a theory about holes is defined over a mereological basis. We also assume primitives for representing shapes of objects (including the string). From these primitives we propose a sufficient condition for object's penetrability through holes. Additionally, a string is represented as a data structure defined upon a sequence of sections limited by points where the string crosses itself or points where it passes through a hole.