Evolved Natural Logic Vs Designed Propositional Logic

Halliday & Matthiessen (1999: 104):

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. […] Since propositional logic is a designed system, its relations are codified and defined (typically in truth-functional terms). 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 peripheral representatives and ‘grey areas’ where one type shades into another. There is another important difference between propositional logic and natural logic of sequences. While there is only a very small handful of truth-functional connectives in propositional logic (conjunction, disjunction [exclusive or non-exclusive], implication), there is a very wide range of sequential relations in language — all the more specific varieties of projecting and expanding.