Halliday & Matthiessen (1999: 104, 104n):
Sequences might be said to constitute the 'natural logic' equivalent of propositional logic — that is, the evolved system for reasoning about relations of cause, conditionality, etc. from which propositional logic has been derived by design. Thus we have parallel series such as:
But, as has often been pointed out, the two are not translation equivalents; for example, material implication (p –> q) applies even when the rendering in ordinary language seems odd, and disjunction in logic is either inclusive or exclusive whereas natural disjunction is non-committal. Since propositional logic is a designed system, its relations are codified and defined (typically in truth-functional terms¹). In contrast, sequential relations have evolved. A certain type of relation will have a core — the prototypical representatives of that type; but there will also be more peripheral representatives and 'grey areas' where one type shades into another.
¹ Propositional logic is interpersonally invariable. Unlike natural logic, it is only concerned with statements, or rather — since language is concerned with validity rather than truth — with the philosophical version of what are statements in natural language.