Posits for ChatGPT

/*
	2023-03-29	Split into several prompts, each less than 2000 characters (Bing limit).
*/
--============ FIRST PROMPT ============--
A posit essentially captures a piece of information. Here are two examples:

p1 = [{(Archie, beard)}, fluffy red, 2020-01-01]

p2 = [{(Archie, husband), (Bella, wife)}, married, 2004-06-19]

The first posit, p1, captures the information that Archie had a fluffy red beard on the 1st of January 2020. The second posit, p2, captures the information that Archie and Bella are married since the 19th of June 2004. Posits can express properties, as in p1, and relationships, as in p2. In transitional modeling, relationships are properties that require more than one thing to take on a value. Such an approach may be unfamiliar, since in most other modeling techniques there are separate constructs for properties and relationships. The proper way to read those two posits, using the notion of roles, is:  When Archie filled the beard role the value ‘fluffy red‘ appeared on 2020-01-01.  When Archie filled the husband role and Bella the wife role the value ‘married‘ appeared on 2004-06-19. A singular thing filling a singular role gives rise to what we usually call properties or attributes, whereas a combination of things filling a combination of roles give rise to relationships. Whenever roles are filled, some value appears. In the case of Bella and Archie it could just as well have been ‘divorced’, ‘planned’, or ‘not applicable’. In fact, for the vast majority of people we could fill the roles with the relationship is ‘not applicable’, but we tend to document these only in the rare cases such posits carry valuable information. Given the terminology of things (Archie, Bellla) and roles (beard, husband, wife), the structure of a posit can be formalized as:

posit = [{(thing 1, role 1), ..., (thing n, role n)}, appearing value, time of appearance]

The set in the first position of the posit is called an appearance set, followed by the for that set appearing value and its time of appearance.

--============ SECOND PROMPT ============--
Posits are just pieces of information and there is no requirement that they must be true. After all, there is a lot of untrue information out there and much more, maybe even most, that is uncertain to some degree. We do not want to disqualify any information from being recorded based on its certainty. Instead, opinions about posits are also captured using posits on the following form:

p3 = [{(p1, posit), (Bella, ascertains)}, 1.00, 2020-01-02]

There is no way to determine its truthfulness from a posit alone, so an additional posit is needed. An assertion is a posit that assigns a certainty to another posit. In the example above, Bella ascertains the posit about Archie’s beard, with absolute certainty on the 2nd of January 2020. Assertions are subjective, and so far we only have Bella’s view of p1. Someone else could disagree with Bella by making a different assertion. Certainty is expressed by a real number in the interval [-1, 1], where 1 is being absolutely certain of what the posit is stating, 0 is having no idea whatsoever, and -1 being certain of the opposite of what the posit is stating. For example, if you want to state that Charlie was not present at the wedding this can be captured using the following posit and later assertion:

p4 = [{(Charlie, participant), (Notre Dame, church)}, present, 2004-06-19]

p5 = [{(p4, posit), (Charlie, ascertains)}, -1.00, 2020-01-02]

In other words, certainty in the range (0, 1] indicate that the asserter is ranging from very unsure (positive and close to 0) to completely certain about what a posit is stating (when 1). Certainty in the range [-1, 0) indicate that the asserter is ranging from completely certain of the opposite of what a posit is stating (when -1) to very unsure about the opposite (negative and close to 0).

--============ THIRD PROMPT ============--
Another important part of modeling is classification. This is again handled using posits, now on the form:

p6 = [{(Archie, thing), (Person, class)}, active, 1972-08-20]

This posit tells us that Archie belongs to the Person class since 1972-08-20, using the class role. Thanks to classification being expressed through posits, it is possible to disagree on these using assertions. It is also possible to have multiple classifications at once and to let classifications expire or become active at different points in time.