Neglect Functions

<< Truth Functions and Their Parses

So far I have only discussed truth functions with operators that are either explicitly defined or completely variable. But what about the myriad forms of uncertainty between? Neglect offers a way, by systematically examining the impact an input variable has on one or more truth functions, while removing it from the problem. The next couple pages will define a neglect function and explore some uses for them.

Neglect Functions
In the first section of this thread, I used specific values assigned to a sequence of input variables to define a condition value. I also used specific values assigned to a sequence of parses to define an operator. If a truth function returns truth for a given condition value, then why not define a function that returns truth for a given operator? A neglect function is just such a function.

At its core, a neglect function is a truth function with a sequence of semi-parses as its domain. This semi-parse domain is a sequence of the semi-parses, for a given parent function, generated by each condition value of a neglected domain.

Here is the parent function and is the neglected domain.

For reasons that will become clear in later examples, a neglect function is not restricted to the semi-parses of a single function. The parent domain may have one or more function in it; the semi-parses of the second parent function simply follow those of the first, and so on.

Writing out all these semi-parses is fun an all, but it doesn’t take long before it’s too much. To stave off writer’s cramp, I write the parent domain between angle brackets, followed by a superscript containing the neglected domain, and a subscript for the neglect function’s operator.

Or, in general, the parent domain and neglected domain can be represented by the same sequence notation used normally for a domain.