Arthur Collings

• The American Society for Cybernetics

This paper establishes representations for modal logics in BF Calculus , an extension to Spencer-Brown's Primary Algebra(Laws of Form). BF is equivalent to a 4-valued bilattice, but the BF formulation provides efficient access to Spencer-Brown's two-valued calculus for modeling the validity of modal axioms and statements.

This paper describes the BF Calculus, a four-valued extension to Laws of Form in which the Law of Crossing is reinterpreted as a cycle of period four. It serves as a companion to the paper entitled The BF Calculus and the Square Root of Negation [9]. BF is built entirely from a single symbol, the imaginary mark, using a notation based on containmen...

The concept of imaginary logical values was introduced by Spencer-Brown in Laws of Form, in analogy to the square root of -1 in the complex numbers. In this paper, we develop a new approach to representing imaginary values. The resulting system, which we call BF, is a four-valued generalization of Laws of Form. Imaginary values in BF act as cyclic...

This article introduces a new 4-valued propositional logical calculus, which we call B4, and establishes its equivalence to the Bilattice FOUR. B4 is shown to satisfy a series of previously unknown identities-identities which cannot be derived on the basis of the axioms of Boolean Algebra, but require the establishment of a previously unknown axiom...

Beginning with the concepts of eigenform and "reflexive domain," Louis Kauffman's target article explores at a deeply abstract level the question of what constitutes second-order science. Kauffman has written a series of papers over the last 10 to 15 years that take as their point of departure the concept of eigenform, returning again and again to...