Generator

kripke

A generator in the logic library, called 3 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.

kripke is one function. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and if the generator changes, this page changes with it.

At its defaults

a chain — where p is necessary and where it is merely possibleA directed graph of worlds with an assignment for p, and the box and diamond values computed at each world.w0w1w2w3worldp□p◇pw0FTTw1TFFw2FTTw3TTFa chain: p is true at w1, w3□p is read off the arrows out of a world, and a world with no arrows out makes □p true for free

show: "stages"

Stages of knowledge, and the stage where p ∨ ¬p is not yet availableA partially ordered set of information stages with p established at some of them, and a table of what each stage forces.w0w1w2w3w4stagep¬pp ∨ ¬pw0w1w2w3yesyesw4yesyesstages of knowledge: an arrow is "later, knowing more", and p is established at w3, w4p ∨ ¬p fails at w0, w1, w2 — p is not established there and never being established is notestablished either

What it checks while it draws

Collected by running the family and recording what it asserted, not written here. The count is how many separate times the claim was put to the test while these drawings were made.

Where it is called

Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.

The whole library · What the figures prove