As an exercise, I would like to write a simple program which will take as inputs three propositions (AEIO) and output true or false based on if the resulting syllogism is valid or not. Obviously, I need a rigorous understanding of exactly when a syllogism is valid. The Wikipedia article (https://en.wikipedia.org/wiki/Syllogism) mentions 256 possible syllogisms out of which 24 are valid. That opens the possibility of a hard-coded table. The following article (http://www.uky.edu/~rosdatte/phi120/lesson17a.htm) speaks of the "rule method" for determining validity but I am unclear if these are merely necessary or sufficient conditions. My question is this: what are the standard tests for syllogism validity? I would ideally like several different options to get a sense of what options are available and which are best for a computer based on different trade-offs.
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This seems to be a method, but I'm not familiar with it. The ref is to H.Gensler, A simplified decision procedure for categorical syllogisms (1973). – Mauro ALLEGRANZA May 07 '18 at 06:52
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I suppose that the procedure implements the traditional "meta-theoric" rules. See Aristotle's Logic : 5.5 Metatheoretical Results : "1. No deduction has two negative premises. 2. No deduction has two particular premises", etc. – Mauro ALLEGRANZA May 07 '18 at 06:54