Hard properties can be assigned to a BF, without referencing its arity.
Integer properties have all non-negative integers as values.

valency ≤ adicity ≤ arity

Valency is the number of atoms, i.e. the number of arguments acutally used. It is the number of circles in the Euler diagram.

Adicity follows from the biggest atom. 2^adicity is the required length of the truth table, or the period length of the infinite truth table.

In this project arity is not a property of a BF. The term is used in two slightly different ways:

• arity n as a shorthand for adicity ≤ n   (as in: the 16 2-ary Boolean functions)
• arity n as an argument to get a finite truth table of length ${\displaystyle 2^{n}}$   E.g. ${\displaystyle B\land C}$ can be shown as 3-ary 0000 0011 or as 4-ary 0000 0011 0000 0011.

This can be explained in terms of object-oriented programming: Valency and adicity are attributes of a BF class. Arity is an argument to some of its methods.

strength

2^strength = family size

gravity and depth

2^gravity and 2^depth are the cardinalities of legion and cohort.
The result for the contradiction is infinity. Soft equivalents have been defined to avoid this problem. Soft gravity is twin valency. Soft depth is related to strength.