van Eijk on Syllogistics

Jan van Eijck. “Syllogistics = Monotonicity + Symmetry + Existential Import”, ms, May 26, 2005.

Abstract: Syllogistics reduces to only two rules of inference: monotonicity and symmetry, plus a third if one wants to take existential import into acccount. We give an implementation that uses only the monotonicity and symmetry rules, with an addendum for the treatment of existential import. Soundness follows from the monotonicity properties and symmetry properties of the Aristotelean quantifiers, while completeness for syllogistic theory is proved by direct inspection of the valid syllogisms. The implementation uses Haskell, and is given in ‘literate programming’ style.