论文标题
部分函数的差异代数：公理和表示形式
Difference-restriction algebras of partial functions: axiomatisations and representations
论文作者
论文摘要
我们研究了具有相对补体和域限制的签名的部分函数代数的表示形式和完整表示类。我们为通过部分函数表示的代数类别提供并证明有限方程公理化的正确性。作为推论，相同的方程式公理将代数表示为射入部分函数。对于完整的表示形式，我们表明，只有在加入完整时，就可以完成符合表示形式。然后，我们表明，完全代表的代数完全是原子和代表代数的类别。作为推论，相同的属性公理化了代数类别完全由凹式部分函数表示。在这些完整表示类别中，通用 - 存在的公理化是最简单的，从某种意义上说，不存在存在的公理存在。
We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational axiomatisation for the class of algebras representable by partial functions. As a corollary, the same equations axiomatise the algebras representable as injective partial functions. For complete representations, we show that a representation is meet complete if and only if it is join complete. Then we show that the class of completely representable algebras is precisely the class of atomic and representable algebras. As a corollary, the same properties axiomatise the class of algebras completely representable by injective partial functions. The universal-existential-universal axiomatisation this yields for these complete representation classes is the simplest possible, in the sense that no existential-universal-existential axiomatisation exists.
