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Glossary

Every term the lessons define, from distinctions and states to refutations and depth.

From John Cullen’s knotlab guide

Distinction. Two alternatives of which exactly one holds: one bit (lesson 1.1).
Joint state. A value for every variable, written as a string such as 110 (lesson 1.1).
Relation. The set of joint states a system of rules allows. Two systems that allow the same states are the same relation (lesson 1.2).
Free. A set of variables is free when every combination of their values occurs in some allowed state. The guide also calls such a set unconstrained, and any other set constrained (lesson 1.2).
Clause. An "or" of letters, each possibly negated, such as ¬A ∨ ¬B ∨ c. It rules out one assignment of its own variables, and a list of clauses that must all hold is a CNF (lesson 1.2).
Emergence. What a system of rules shows as a whole and none of its rules shows alone, as the Game of Life's patterns do on a grid (lesson 1.3). The program places the first emergence at the first knot.
Loop. A logical structure that leaves a distinction open (lesson 1.4).
Contact. The variable through which loops are bound (lesson 1.4).
Atom. The knot ¬A ∨ ¬B ∨ c: the smallest bond. It is also written A ∧ B → c, or A, B → c, and read "A and B together demand c": it forbids only the state with A and B but not c (lesson 1.5).
Forgetting. Ignoring a variable: a state of the others stays allowed when some value of the forgotten one completes it. What remains is the projection, or shadow, on the others (lesson 1.6).
Witness. An auxiliary variable that reports on something, such as whether two loops are bound. Witnesses are quantified away before a verdict (lesson 1.6).
Knot. A relation that is constrained as a whole and unconstrained in every part (lesson 2.1).
Hub. One variable shared by several separate relations, such as (¬A ∨ c) ∧ (¬B ∨ c). Sharing identity is not a binding (lesson 2.1).
Majority. The state that takes, in each variable, the value at least two of three given states take. Systems of two-place rules are closed under it, and knots are not (lesson 3.1).
Shape. The simplicial complex of sets of distinctions a system leaves free. A hole is a gap in it, and a knot is the smallest kind of hole (lesson 3.3). In the broad sense of lesson 1.7, any structure that rules make.
World. With 1 read as "exists", the set of things that exist in an allowed state (lesson 4.2).
Requirement. A rule saying what must exist when other things do, such as A ∧ B → c. A choice says that when something exists, one of several things must, such as c → A ∨ B (lesson 4.2).
Refutation. A proof that a system allows no state at all (lesson 5.1).
Depth. How much of a network an observer must hold at once to see a hole in it (lesson 5.2).