Sylogistyka jako fragment ontologii elementarnej

  • Eugeniusz Wojciechowski

Abstrakt

Five interpretations of syllogistic in Leśniewski's ontology are presented in the paper. Two of them are weak (φw) and strong (φs) interpretations of syllogistic (without negative terms) in ontology. The remaining are called here intermediate ones.

The first of them (φm), formulated by Iwanuś, is also an interpretation of syllogistic without negative terms. The last two intermediate interpretations (φn, φo) are interpretations of syllogistic with negative proposed by the author.

Assuming a help functor of coexistence:

coex(x,y) ↔ (ex(y) → ex(x)). (ex(nx) → ex(ny))

the φn interpretation has the following form:
xaycoex(x,y). x y
xey
coex(x,ny). x ny
xiy
↔ (coex(x,ny) → Σz(zεx. zεy))
xoy ↔ (coex(x,y) → Σz(zεx. zε‾x))
The interpretation φo is a variant of φn.

It is proofed that syllogistic by the interpretation φm is a fragment of elementary ontology and that the syllogistic with negative terms by interpretations φn and φo is inferentially included in this system with no empty universe.

Opublikowane
2020-11-13
Dział
Artykuły