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> Is it simply a different and consistent notation, or is there more to it?

I've found that you can use that question to partition people (who have an opinion on the question) into two major groups: Those who dismiss LoF as just another notation, and those who do find something deeper in it or at least claim to.

Pragmatically it's strictly superior to conventional notation: it's more parsimonious and it admits the rule (due to W. Bricken, I believe):

    A(AB) = A(B)
Which is unknown in other notations, and permits proofs in LoF notation to be extraordinarily concise and elegant (compared to proofs worked in conventional notation.) It also permits a concise implementation of a SAT solver that has the nice property that you don't have to put your problem into normal form.

Recently, George Burnett-Stuart (not Spencer-Brown), the author of the "Markable Mark" site, has worked out how to encode Predicate Calculus http://www.markability.net/prospectus.htm

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