We propose that textual style should be best defined as non-denotational meaning, i.e., those aspects of a text’s meaning that are mostly independent of what the text refers to in the world. To make this more concrete, we describe a linguistically well-motivated framework for computational stylistic analysis based on Systemic Functional Linguistics. This theory views a text as a realisation of multiple overlapping choices within a network of related meanings, many of which relate to non-denotational (traditionally `pragmatic') aspects such as cohesion or interpersonal distance. Variations between relative frequencies of options within these systems corresponds to stylistic variation. Though full parsing in SFL remains a difficult unsolved problem, we present a software architecture which allows for efficient modelling and extraction of SFL entities for use in stylistic analyses. In support, we show results for two applications: classifying texts as financial scams and classifying scientific articles by field.