Halliday & Matthiessen (2014: 324):
Accompaniment is a form of joint participation in the process and represents the meanings ‘and’, ‘or’, ‘not’ as circumstantials … We can distinguish two subcategories, comitative and additive; each has a positive and negative aspect. … A circumstance of Accompaniment may have an additional sense of cause or contingency — ‘since/if x has/hasn’t’.