GFO Part I Basic Principles
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7.1 Material Structures, Space, and Time

A material structure $S$ is a presential; hence, it exists at a time-point $t$, denoted by $\Gat(S,t)$. Furthermore, a material structure $S$ exhibits the ability to occupy space. This ability is based on an intrinsic quality of $S$, which is called its extension space or inner space. The relation $\Gextsp(e,S)$ defines the condition that $e$ is the extension space of $S$, and the extension space is regarded a quality similar to its weight or size.

Every material structure $S$ occupies a certain space-region that exhibits the basic relation of $S$ to space. The relation $\Gocc(x,y)$ describes the condition that the material structure $x$ occupies the space-region $y$. A material structure $S$ is spatially contained in the space-region $y$, if the space-region $x$ occupied by $S$, is a spatial part of $y$. In this case we say that $x$ is the spatial location of $S$ with respect to $y$. The relation $\Gocc(x,y)$ depends on granularity; a material structure $S$, for example, may occupy the mereological sum of the space-regions occupied by its atoms or the convex closure of this system. We assume that in our considerations the granularity is fixed, and - based on this dimension - that the space-region occupied by a material structure is uniquely determined.

For $\Gocc(x,y)$, we may ask whether for every spatial part of $y$ there exists a uniquely determined material structure $z$ that occupies $y$. In this case $z$ is called a material part of $x$; this relation is denoted as $\Gmatpart(z,x)$. Such a strong condition is debatable because it might be that the substrate that a material structure comprises has non-divisable atoms. For this reason we introduce the relation $\Gmatpart(z,x)$ as a new basic relation, and stipulate the axiom that $\Gmatpart(z,x)$ implies that the region occupied by $z$ is a spatial part of the region occupied by $x$. Because granularity plays a role here, we separately stipulate to this condition for every fixed occupation-relation separately.

A spatial region $T$ frames a material structure $S$ if the location that $S$ occupies is a spatial part of $T$. Material structures may be classified with respect to the mereotopological properties of their occupied space regions. A material structure is said to be connected if its occupied region is a topoid.

Robert Hoehndorf 2006-10-18


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