Define grammar with a proper parsing state machine

[joedougherty]

Consider using an existing token parsing library to define semantics for sentential logic.

pyparsing is one reasonably good-looking option.

[joedougherty]

Looks like parsimonious (https://github.com/erikrose/parsimonious) might be a reasonable option.

Example here: https://gist.github.com/joedougherty/bc8714cf14898b30951ec1b67345efef