On a Categorical Framework for Coalgebraic Modal Logic
On a Categorical Framework for Coalgebraic Modal Logic
复制标题
代数模态逻辑的分类框架
DOI：
10.1016/j.entcs.2014.10.007
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发表时间：
2014
影响因子：
--
通讯作者：
Chen L
中科院分区：
文献类型：
--
作者：
Chen L
一类一步语义的引入，以统一不同的方法，共代数逻辑参数的逆变函子，分配给状态空间的集合的谓词与命题连接词。模块化结构的coalgebraic逻辑被确定为colimits，限制，和张量积，扩展已知的结果谓词提升。引入模态时的广义谓词提升。在一般的假设下，对于任何类型的余代数，都存在所有谓词提升的逻辑以及完备的公理化，并且对于有限函子，它是一步表达的。一步表达的余代数逻辑的余极限和组合物被证明是保持一步表达。
A category of one-step semantics is introduced to unify different approaches to coalgebraic logic parametric in a contravariant functor that assigns to the state space its collection of predicates with propositional connectives. Modular constructions of coalgebraic logic are identified as colimits, limits, and tensor products, extending known results for predicate liftings. Generalised predicate liftings as modalities are introduced. Under common assumptions, the logic of all predicate liftings together with a complete axiomatisation exists for any type of coalgebras, and it is one-step expressive for finitary functors. Colimits and compositions of one-step expressive coalgebraic logics are shown to remain one-step expressive.