Lewis & Short

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argūmentābĭlis, e, adj. [argumentum], that may be proved: propositio difficile argumentabilis, Boëth. Arist. Anal. 1, 27.

* argūmentālis, e, adj. [argumentum], containing proof: narratio, Ascon. ap. Cic. Div. in Caecil. 1.
Adv.: argūmentālĭter, by way of proof, Aggen. Urb. Com. ap. Front. p. 64 Goes.

argūmentātĭo, ōnis, f. [argumentor] (a rhet. t. t., most freq. in Cic.).

  1. I. An adducing of proof, an argumentation: argumentatio nomine uno res duas significat, ideo, quod et inventum aliquam in rem probabile aut necessarium, argumentatio vocatur et ejus inventi artificiosa expolitio, Cic. Inv. 1, 40: argumentatio est explicatio argumenti, id. Part. Or. 13: perspicuitas argumentatione elevatur, id. N. D. 3, 4, 9: probabilis, id. Fin. 5, 4, 9: expositio verbosior quibusdam argumentis, argumentis dico, non argumentatione, Quint. 4, 2, 79; 5, 14, 35; 11, 3, 164 al.
  2. II. The proof itself: etiamne in tam perspicuis rebus argumentatio quaerenda est aut conjectura capienda? Cic. Rosc. Am. 35.

argūmentātor, ōris, m. [argumentor], he that adduces proof, an arguer; only in Tert. Anim. 38; id. Res. Carn. 24.

* argūmentātrix, īcis, f. [argumentator], she that adduces proof, a female arguer, Tert. Spect. 2.