论文标题
在（$π$ - ）机构理论中连接抽象逻辑和辅助：一些理论备注和应用
Connecting abstract logics and adjunctions in the theory of ($π$-)institutions: some theoretical remarks and applications
论文作者
论文摘要
在当前的工作中，\ cite {mapi1}的自然续集，我们进一步讨论了机构类别和$π$ - 义务之间的辅助。这是在基础和应用水平上完成的。首先，我们从涉及类似机构的结构类别构建的$ 2 $分类数据的角度来重新重新阐明和概念上阐明了此类附件。更准确地说，我们指出的是，用于从房间到机构的过程（\ cite {diac2}），由于其$ 2 $ - 函数的函数，可以扩展到更通用的房间和类似机构的结构，以使上述套头在室内式的简单辅助级别上都出现。其次，主要是独立的，我们为抽象逻辑提供了此类附件的某些应用，主要是为命题逻辑和过滤对的设置（\ cite {amp1}）;我们还概括了从谓词逻辑到制度设置的经典设备Skolemization的过程。
In the present work, a natural sequel to \cite{MaPi1}, we further discuss the existence of adjunctions between categories of institutions and of $π$-institutions. This is done at both a foundational and an applied level. Firstly, we reformulate and conceptually clarify such adjunctions in terms of the $2$-categorical data involved in the construction of categories of institution-like structures. More precisely, we remark that the process used for passing from rooms to institutions (\cite{Diac2}) can be extended, due to its $2$-functoriality, to more general room-like and institution-like structures in such a way that the aforementioned adjunctions are all seen to arise from simpler adjunctions at the room-like level. Secondly, and mostly independently, we provide some applications of such adjunctions to abstract logics, mainly to the setting of propositional logics and filter pairs (\cite{AMP1}); we also generalize the process of skolemization, a classical device from predicate logic, to the institutional setting.
