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100 Modern Spatiotemporal Geostatistics — Chapter 4
(a)
(a)
Xdata('S) X k Xdata(^) "" * X k Xk\Xdata(^)
T T T T
T F F F
F T T
F F T
(b)
XdataiS) Xk Xdata('S) ~^ Xk Xk\Xdata(-S) (b)
T T T T
T F F F
Figure 4.2. Truth tables of spatiotemporal mapping: (a) given ^; (b) given
Other map conditionals
Material map conditionals are expressed in terms of truth-functional concepts,
which implies that the connective "if, then" is used to express the (truth-
functional) concept of material conditionality and this concept alone. As al-
ready mentioned, there exist other important uses of conditionals which are
not based on purely truth-functional concepts, but which express more than
a mere truth-functional relation. These non-truth-functional map conditionals
may assert stronger (physical or logical) connections between Xdata(S) an< ^ Xk
than the purely truth-functional relation of material conditionality. In the case
of a logical map conditional, the antecedent logically implies the consequent.
A physical map conditional is one in which the antecedent physically implies
the consequent. In this sense, and since in the mapping case the \ data(S) and
X k represent the same natural variable, it is likely that the material conditional
Xdata(S] -» Xk expresses a physical connection.
It is a result worth mentioning that, in many cases, no mapping relationship
expressed as any sort of conditional (physical, logical, etc.) is valid unless the
same relationship viewed as a material conditional is valid. In other words, if
the relation "Xdata(S) implies Xk" ' s n °t valid when considered as a material
conditional, then it is also not valid when considered as a physical or a logical
conditional. As a consequence, the following postulate seems justified.
POSTULATE 4.2: Even though most of the conditionals we encounter
in natural sciences are physical or logical conditionals, the material con-
ditionals can play a basic role in modern geostatistics.
The preceding discussion remains valid in the case of two or more natural
variables, as illustrated with the help of the following example.
