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i'd like to contribute with two sugestions you might find interesting:
- the notation used by g. spencer brown in his Laws of Form
- charles sanders peirce investigation and comments on the subject on his On the Algebra of Logic: A Contribution to the Philosophy of Notation published on the American Journal of Mathmatics
on a computational linguistic level, i'd like to point out also panini's monumental Ashtadhyayi, a generative grammar for sanskript allowing it to produce any valid statement in sanskrit with a strictly concise set of rules. it is compared to modern notations like BNF and considered to be an ancient turing machine and computing language as this set of rules are said to be turing complete. panini might properly be called with justice the euclid of linguistics
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