The reciprocal construction is an adverbial clause (v. 'each to the other(s)', 'the one to the other(s)') within which 'each other' is resolved as two quantifiers, a distributive 'each of them' and a definite description 'those other than them' or 'those other than that'. Variation in the meaning of reciprocal constructions derives from pragmatic conditions on adverbial modification, the resolution of the descriptive anaphora restricting the reciprocal's quantifiers, and the intention to describe one of many events. The reciprocal presents itself without any further structural or lexical ambiguity.
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