GFO Part I Basic Principles
           
  ontomed Theories Concepts Applications  
 
Ontological
Investigations
Conceptual
Modelling
Onto-Builder
 
 
Axiomatic
Foundations
Domain
Ontologies
Onco-Workstation
 
 
Metalogical
Analyses
Ontology
Languages
SOP-Creator
 
           
 
 

Onto-Med >> Theories >> GFO Part I Basic Principles

 
    Subsections

14.7 Relation of Concrete Individuals to Space and Time

Concrete individuals have a relation to time or space.

14.7.1 Material Structures

Material structures are presentials, hence they exists at a time-point, and the relations $\Gat(m,t)$ captures this relation. The relation $\Gat(m,t)$ is functional, hence a presential $m$ cannot exist at two different time-points.

The binary relation of occupation, $\Gocc(x,y)$, describes a fundamental relation between material structures and space regions. Occupation is a functional relation because it relates an individual to the minimal topoid in which a material structure is located. Location is a less detailed notion, which can be derived in terms of occupation and spatial part-of. An $x$ is located in a region $y$, $\Gloc(x, y)$, iff the topoid $z$, occupied by $x$, is a spatial part of $y$.

14.7.2 Processes

Every process has a temporal extension. This temporal extension is called the projection of the process to time, and is denoted by $\Gprt(x,y)$. We distinguish several cases: $\Gprt(x,c)$, $\Gat(y,t)$, $\Gprb(x,t,y)$, where $x$ is a process, $y$ is a presential, $c$ is a chronoid, and $t$ is a time-boundary. The binary relations assign a temporal entity to presentials and processes, while $\Gprb(x,t,y)$ is the projection of a process $x$ to its boundary $y$, which is determined by the time-boundary $t$. Note that $\Gprb$ can be used to define the relations $\Gat$ and $\Gpartic$.

14.7.3 Framing

Every situoid, for example the fall of a book from a desk, occurs over time and occupies a certain space. The binary relations of framing, such as $\Gtframe(s,
c)$, $\Gsframe(s,x)$ binds chronoids $c$ or topoids $x$ to situoids $s$. We presume that every situoid is framed by exactly one chronoid and one topoid. The relation $\Gtframe(s, z)$ / $\Gsframe(s, z)$ is to be read: ``the chronoid / topoid $z$ frames the situoid $s$''.

Robert Hoehndorf 2006-10-18
 
       
     
     
     

   
     
     
       
 

deutsch   imise uni-leipzig ifi dep-of-formal-concepts