By converting one or both of the premisses we may at once deduce from the above a table of valid (unstrengthened and unweakened) moods for all four figures as follows:—
| Fig. 1. | Fig. 2. | Fig. 3. | Fig. 4. |
| AAA | YAA | AYA | YYA |
| YYY | AYY | YAY | AAY |
| EAE | EAE | EYE | EYE |
| YEE | AEE | YEE | AEE |
| AII | YII | AII | YII |
| IYI | IYI | IAI | IAI |
| EIO | EIO | EIO | EIO |
| YOO | AOO | YηO | AηO |
| OYO | ηYO | OAO | ηAO |
| IEη | IEη | IEη | IEη |
| ηAη | OAη | ηYη | OYη |
| Aηη | Yηη | AOη | YOη |
II. The above table may also be obtained by (1) taking all the combinations of premisses that are à priori possible, (2) establishing special rules for the particular figure selected, which (taken together with the rules of quality) will enable us to exclude the combinations of premisses which are either invalid or strengthened whatever the conclusion may be, (3) assigning the valid unweakened conclusion in the remaining cases.
384 The following are all possible combinations of premisses, valid and invalid:
| AA (b) | YA | IA | EA (b) | OA | ηA(b) (c) |
| AY | YY (a) | IY (a) | EY | OY (a) | ηY |
| AI | YI (a) | II (a) | EI | OI (a) | ηI (c) |
| AE (b) | YE | IE | [EE] (b) | [OE] | [ηE] (b) |
| AO | YO (a) | IO (a) | [EO] | [OO] (a) | [ηO] |
| Aη (b) (c) | Yη | Iη (c) | [Eη] (b) | [Oη] | [ηη] (b) (c) |
The combinations in square brackets are excluded by the rule that from two negative premisses nothing follows.
Taking the third figure, in which the middle term is subject in each premiss, and remembering that the subject is distributed in A, E, η and in these only, while the predicate is distributed in Y, E, O and in these only, the following special rules are obtainable:
(a) One premiss must be A, E, or η, or the middle term would not be distributed in either premiss;
(b) One premiss must be Y, I, or O, or the middle term would be distributed in both premisses, and there would hence be a strengthened premiss;
(c) If either premiss is negative, one of the premisses must be Y, E, or O, for otherwise (since the conclusion must be negative, distributing one of its terms) there would be illicit process either of major or minor.