I believe semiotics is the philosophical branch of applied linguistics.
A few names come to mind although I can't say whether they are the
'founders' - Roland Barthes, Jacques Derrida, Michel Foucault and Jean
Baudrillard. I believe Noam Chomsky is also a person you may be
interested in reading. His research regarding language and meaning is
quite interesting. He is responsible for the theory of the 'language
acquisition device' - that there is a certain 'switch' in the brain that
is triggered at a certain time - that then becomes atrophied to some
extent as a person gets older.