The Ars demonstrativa was the second version of the Lullian Ars, and revised and completed the Ars compendiosa inveniendi veritatem (1274). It was composed in Montpellier in 1283. The work is accompanied by Figures and an Alphabet; the former are graphic symbols which make the structural components of the Ars visible and facilitate the operation of the combinatorial mechanisms and the calculations. As regards the Alphabet, the letters A S T V X Y and Z represent the Figures mentioned above, while the others – namely those between B and R – serve to designate the concepts contained within Figure S, the figure pertaining to the rational soul.

The Ars demonstrativa has four parts or ‘distinctions’, of which the final part is a list of questions relating to the preceding parts, accompanied by their corresponding solutions in symbolic notation. The first distinction gives a detailed description of the figures. The second distinction expounds the ‘conditions’ of the Ars, the mechanisms which enable the reader to obtain information on the basis of the principles from Figures A V X, with a view to discovering the truth or falsity – Figures Y Z – by using Figures T and S, which establish relationships between the principles. The third distinction offers sixteen modes, or rather, applications for the mechanisms of the Ars, which are: remembering, understanding, loving, believing, contemplating, finding, ordering, preaching, expounding, resolving, judging, showing, disputing, advising, accustoming, curing.