Formal language is the set of words that are generated from production rules. There are 2 kind of operations on such language:
application of production rules to generate new (grammatically valid) word from the existing words;
application of inference rules to generate new (grammatically and semantically valid) word (it can be called sentence as well in some settings) from the existing (grammatically and semantically valid) words.
So - there are 2 kind of operations: 1) application of production rules; 2) application of inference rules (subset of production rules?).
My question is - how those grammatical/inferential operations are connected to the algebra? Does the grammar of the formal language define special algebra of words? Are the operations of this algebra connected to the grammatical/inferential operations of the language? Is algebra used for modelling the formal language?
I feel that there is some connection but I am really confused.
Maybe term algebra is the answer?