Volume 2 builds on the foundation developed in Volume 1, focussing on theoretically guided modelling of language in computational linguistic systems and on key aspects of the theory such as metafunction, rank (the conception of "morphology"), indeterminacy and probability. This volume also includes a treatment of systemic functional meta-theory - the theory of the nature and appliability of theory. The new chapter written for Volume 2 extends the discussion of the challenge of theorizing language to the challenge of modelling language for neurosemiotics, thus paying attention to the appliability of systemic functional linguistics.