Indicator Functions • Discussion

[Jon Awbrey]

Ontolog Forum, Sys Sci, Structural Modeling Groups,

Peter Smith, on his Logic Matters blog, asks the question,
“What is a Predicate?”, and considers a number of answers.

• https://www.logicmatters.net/2018/10/09/what-is-a-predicate/

There are of course other possible answers, and one I learned quite early on,
arising very naturally in applying mathematical logic to what were generally
known as “AI problems”, like perception and pattern recognition, and the one
I found increasingly useful as I took up the reflective stance on symbolic
computation afforded by Peirce's pragmatic semiotics, I described this way:

In many applications a “predicate” is a function from a universe of discourse X
to a binary value in B = {0, 1}, that is, a characteristic function or indicator
function f : X → B, and f⁻¹(1), the “fiber” of 1 under f, is the set of elements
denoted or indicated by the predicate. That is the semantics, anyway. As far as
syntax goes, there are many formal languages whose syntactic expressions serve
as names for those functions and nominally speaking one may call those names
“predicates”.

Regards,

Jon

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[joseph simpson]

Jon:

Very interesting point of view.

From the referenced post:

"A predicate is just an expression, as in ‘is wise’ in the ordinary language sentence ‘Socrates is wise’, or ‘loves’ in Romeo loves Juliet’ — an expression which can combine with names or other suitable expressions to form sentences."

In structural modeling, predicates like: "is bigger than", "in the same category as". "influences" and "north of" are used to structure the complete collection of objects.  The structuring may be conducted by evaluating the predicate for two objects at a time. 

The number of objects, in the collection, that must be empirically evaluated to completely structure the collection depends on the logical properties of the predicate statement.  A binary matrix is commonly used to represent the  structure of the system.  

Structural modeling is focused on the static state of a system.  System behavior may be modeled using similar methods and processes, however, the content on the predicate statements are different.

Take care, be good to yourself and have fun,

Joe

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Joe Simpson

“Reasonable people adapt themselves to the world. 

Unreasonable people attempt to adapt the world to themselves. 

All progress, therefore, depends on unreasonable people.”

George Bernard Shaw