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A last type of inference is called contraposition and is produced by the fact that some propositions imply the proposition that results from the original proposition when both of its term variables are negated and their order reversed.
Using the notation of the early 20th-century logician Jan Łukasiewicz, the general terms or term variables can be expressed as lowercase Latin letters a, b, and c, with capitals reserved for the four syllogistic operators that specify A, E, I, and O propositions.
bThe category Others include the Region of residence, Urban area, Married and the Constant term variables.
Let the formulas (lower-case letters are term variables) Uab, Iab, Yab, Oab stand for the sentences "every a is b", "some a are b", "no a is b" and "some a are not b".
The axioms are as follows: (a) Uaa; (b) Iaa; (c) CKUmbUamUab (the Barbara modus); (d) CKUmbImaIab (the Datisi mode); the rules are: all the rules of propositional calculus, substitution for term variables, the definitional replacement according to the definitions of Yab and Oab.
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