Re: Ontolog Forum • Joseph Simpson
Re: Animated Logical Graphs • 21
I invoked the general concepts of equivalence and distinction at this point in order to keep the wider backdrop of ideas in mind but since we’ve been focusing on boolean functions to coordinate the semantics of propositional calculi we can get a sense of the links between operations and relations by looking at their relationship in a boolean frame of reference.
Let 
- A
-variable boolean function is a mapping
- A
-place boolean relation is a subset of
The correspondence between boolean functions and boolean relations may be articulated as follows:
- Any
-place relation
as a subset of
has a corresponding indicator function (or characteristic function)
defined by the rule that
if
is in
and
if
is not in
- Any
-variable function
is the indicator function of a
-place relation
consisting of all the
in
where
The set
is called the fiber of
or the pre-image of
in
and is commonly notated as
as a subset of 
has a corresponding indicator function (or characteristic function) 
defined by the rule that 
if 
is in 
and 
if 
is the indicator function of a 
consisting of all the 
The set 
or the pre-image of 
cc: Systems Science • Structural Modeling • Ontolog Forum • Laws of Form • Cybernetics
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