A formal system consists of a notation and a system of transformations. Boundary logic is unique in that the notation sheds light on different ways to use logic. It also facilitates new and different proof techniques.

Boundary logic is algebraic, it uses equality and substitution-of-equals as the primary computational technique. However boundary computation and proof have several unique features, including the semantic use of non-representation (the <void>), and deep rules that treat nested boundaries and boundary forms transparently, as if they were not there.

Two pieces introduce boundary logic computation:

BOUNDARY LOGIC TRANSFORMATION –– Short descriptions and examples of the axioms and transformation systems of boundary logic.

COMPARISON TO CONVENTIONAL LOGIC –– Boundary logic can, of course, be interpreted as, or transcribed into, conventional logic. However, the transcription is not one-to-one, it is one-to-many. This means that boundary logic is not isomorphic to conventional logic, rather it is formally simpler. This section provides comparisons to other logical techniques.

COMPLEXITY –– Several monographs on generalized insertion and how Losp handles complexity in logical tautologies.

PREDICATE LOGIC –– Adding theories of quantification, equality, functions and relations to boundary logic.