Oblique Syllogisms

Abstract

The aim of this paper is the analysis of so-called oblique syllogisms. Its consequence is the proposal of such an extention of the syllogistic with negative terms, including inferences with syllogism of this type. It considers following the two such extentions, where the first is inferentially contained in the second one.

The second of those calculi with the axiom system: xanny, ∼(xanx), nxany → yax, xay ⋅ yaz → xaz, xay → fxafy and the definitions: xey ↔ xany, xiy ↔ ∼(xany), xoy ↔ ∼(xay), besides the inferential rules common with syllogistic and the rule of substitution for functors (without nominal negation), has the specific extended rule of substitution: for the simple nominal variables of the type „x” it may substitute besides the other simple nominal variables, also those composed with negation of the kind „ny”, as well as the composed variables of the type „fy”, with „f” different from „n”. The interpretation of those calculi in protothetic is given.