论文标题
S5模式Gödel逻辑的代数研究
An algebraic study of S5-modal Gödel logic
论文作者
论文摘要
在本文中，我们继续研究MonadicGödel代数的品种$ \ Mathbb {mg} $。这些代数是Gödel逻辑S5模式扩展的等效代数语义，该语义与一阶Gödel逻辑的一阶单元片段相当。我们向$ \ mathbb {mg} $的三个本地有限次群的家庭展示了他们的方程基础。我们还引入了MonadicGödel代数的拓扑二元性，作为该表示定理的应用，我们表征了一致性，并通过其双重空间来表征上面提到的本地有限的亚Varieties。最后，我们研究了由MonadicGödel链产生的亚变量的一些进一步的特性：我们为该品种提供了一个特征性链，我们证明了Glivenko-type定理为这些代数构成，并且我们表征了$ N $ Generator的自由代数。
In this paper we continue the study of the variety $\mathbb{MG}$ of monadic Gödel algebras. These algebras are the equivalent algebraic semantics of the S5-modal expansion of Gödel logic, which is equivalent to the one-variable monadic fragment of first-order Gödel logic. We show three families of locally finite subvarieties of $\mathbb{MG}$ and give their equational bases. We also introduce a topological duality for monadic Gödel algebras and, as an application of this representation theorem, we characterize congruences and give characterizations of the locally finite subvarieties mentioned above by means of their dual spaces. Finally, we study some further properties of the subvariety generated by monadic Gödel chains: we present a characteristic chain for this variety, we prove that a Glivenko-type theorem holds for these algebras and we characterize free algebras over $n$ generators.
