Tree proofs for syllogistic (Q918950)

The author presents a method of tree-proof for syllogistic similar to that often taught for the propositional calculus. No propositional calculus is included here, however. Categorical propositions are formed with the existential (I) operator, the emptiness (E) operator, simple- term negation, and multiple conjunction of simple terms and their negatives. The elegant proof procedure is shown to be both sound and complete. Syllogisms both with and without existential import, as well as sorites, are treated. The two syllogistic operators employed are suggested by the work of F. Brentano. As the author points out, the tree method is more efficient than other common methods of testing syllogisms, such as Venn and Lewis Carroll diagrams. It is not quite so easy, however, as F. Sommers' additive method.