瓦伊斯堡环的多面体几何
The polyhedral geometry of Wajsberg hoops
摘要：
我们证明了具有同态的Wajsberg环的范畴对偶等价于具有Z-映射的有理多面体的一个特殊子范畴。我们使用的对偶性，以提供一个几何特征的生成的投影和确切的Wajsberg箍。作为应用，我们研究了Lukasiewicz逻辑正片段的逻辑性质.我们表明，而演绎的片段是等价的演绎正公式在Lukasiewicz逻辑，同样是不真实的规则的可接受性。此外，我们还证明了Wajsberg环的统一类型是零元的，而精确统一类型是酉的，从而证明了片段中可容许规则的可判定性。
英文摘要：
We show that the category of finitely presented Wajsberg hoops with homomorphisms is dually equivalent to a particular subcategory of rational polyhedra with Z-maps. We use the duality to provide a geometrical characterization of finitely generated projective and exact Wajsberg hoops. As applications, we study logical properties of the positive fragment of Lukasiewicz logic. We show that, while deducibility in the fragment is equivalent to deducibility among positive formulas in Lukasiewicz logic, the same is not true for admissibility of rules. Moreover, we show that the unification type of Wajsberg hoops is nullary, while the exact unification type is unitary, therefore showing decidability of admissible rules in the fragment.
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