Physical Distance Function
Jump to navigation
Jump to search
A Physical Distance Function is a Vector Distance Function for the Real World.
- AKA: Physical Distance, Spatial Unit.
References
- http://www.isi.edu/~hobbs/bgt-space.text
- In the predicate "distance", we take d to be a non-negative number dependent upon the spatial unit u that is used, rather than reifying distances as distinct entities. We won't say what a spatial unit is, but it can be characterized in the same way temporal units were characterized in Chapter B12. The constraints on the arguments of "distance" are as follows:
(2)
- In the predicate "distance", we take d to be a non-negative number dependent upon the spatial unit u that is used, rather than reifying distances as distinct entities. We won't say what a spatial unit is, but it can be characterized in the same way temporal units were characterized in Chapter B12. The constraints on the arguments of "distance" are as follows:
(forall (d x1 x2 u s)
(if (distance d x1 x2 u s)
(and (nonNegativeNumber d)(spatialSystem s)
(componentOf x1 s)(componentOf x2 s)
(spatialUnit u s))))
- We will constrain the predicate "distance" by the usual mathematical properties. The distance between an entity and itself is zero.
(3)
- We will constrain the predicate "distance" by the usual mathematical properties. The distance between an entity and itself is zero.
(forall (x u s) (distance 0 x x u s))
- The distance between two entities is symmetric.
(4)
- The distance between two entities is symmetric.
(forall (d x1 x2 u s)
(iff (distance d x1 x2 u s)(distance d x2 x1 u s)))
- The triangle inequality holds.
(5)
- The triangle inequality holds.
(forall (d1 d2 d3 d4 x1 x2 x3 u s)
(if (and (distance d1 x1 x2 u s)(distance d2 x2 x3 u s)
(distance d3 x1 x3 u s)(sum d4 d1 d2))
(leq d3 d4)))