A denial of liability under s 151C(2)(a) must be unequivocal and is assessed objectively; silence, equivocation, or failure to volunteer liability is insufficient. Payment of statutory workers' compensation does not constitute a partial admission of liability under s 151C(2)(b), because 'liability' in s 151C(2) refers exclusively to liability for modified common law damages. 'Partial liability' in s 151C(2)(b) refers to acceptance of liability subject to a dispute about apportionment (such as contributory negligence), not to admission of constituent facts of a cause of action.
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