Presenting Functors by Operations and Equations
Presenting Functors by Operations and Equations
复制标题
通过运算和方程展示函子
DOI：
10.1007/11690634_12
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
A. Kurz
中科院分区：
文献类型：
--
作者：
M. Bonsangue;A. Kurz
我们的观点是，如果转移系统是函子T的余代数，那么这些转移系统的适当逻辑应该产生于T的“Stone对偶”L。我们表明，这样的函子总是产生一个“抽象的”足够的逻辑T-余代数和调查在何种情况下，它产生了一个“具体的”这样的逻辑，即，一个逻辑与归纳定义的语法和证明系统。我们得到一个结果，使我们能够证明充分的逻辑一致的大量不同类型的过渡系统，并给出了一些例子，它的有用性。
We take the point of view that, if transition systems are coalgebras for a functor T, then an adequate logic for these transition systems should arise from the ‘Stone dual' L of T. We show that such a functor always gives rise to an ‘abstract' adequate logic for T-coalgebras and investigate under which circumstances it gives rise to a ‘concrete' such logic, that is, a logic with an inductively defined syntax and proof system. We obtain a result that allows us to prove adequateness of logics uniformly for a large number of different types of transition systems and give some examples of its usefulness.