Abstract
Abstract Aristotelian syllogisms are represented by small oriented graphs. The premisses determine the graph and the conclusion is a property of this graph characterized by only two predicates, namely before and common-before . A search based on this approach yields 18 valid Aristotelian syllogisms. We can get all 24 Aristotelian syllogisms by using the predicate common-edge-star instead of common-before as a modification of the former one. With a possible exception of BAMALIP we suspect that the additional syllogisms discovered by scholastics originated in the extended model, as the new predicate needs a more sophisticated mental representation than the original one. In spite of the criticism of Johnson-Laird we take Aristotelian syllogisms for a very fundamental tool of mental processes, not along the classical formulae but based on some graphical representation. Our two background models described as programs in PROLOG are proposed as two possibilities of this approach.
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