It turns out that a part of what I''m working on is called a ''reasoning program''. I believe I''ve gotten most of the language constructs, but probably not well. Also, several constructs(probability, goals, and belief) are all handled by the same operator. Could that cause problems? Also, are there any complete mathematical descriptions of English grammar so I can more easily translate between the program''s internal language and English? Any help, sources, links, papers, etc. that anyone can recommend?

There is a whole field of research based on formalizing the representation of the English language, search for Natural Language Recognition and you should get a tonne of results.