论文标题
Wajsberg箍的多面部几何形状
The polyhedral geometry of Wajsberg hoops
论文作者
论文摘要
我们表明，具有同态的有限呈现的Wajsberg篮球类别与具有Z-Maps的理性Polyhedra的特定子类别相当。我们使用二元性来提供有限生成的投影和精确的Wajsberg箍的几何表征。作为应用，我们研究了Lukasiewicz逻辑正面片段的逻辑特性。我们表明，虽然片段中的可得到性等于Lukasiewicz逻辑中正式的阳性公式中的可推迟性，但对于规则的可接受性而言并非如此。此外，我们表明Wajsberg箍的统一类型为无效，而确切的统一类型是单一的，因此在片段中显示了可接受的规则的可决定性。
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.
