论文标题
代数可弱逻辑
Algebraizable Weak Logics
论文作者
论文摘要
我们将抽象代数逻辑的框架扩展到弱逻辑，即不一定在统一取代下关闭的逻辑系统。我们解释了代数的弱逻辑，并通过额外的谓词扩展，并为弱逻辑引入了宽松而严格的代数性。我们通过研究弱逻辑的代数性和其原理图片段的代数能力之间的联系来研究此框架，然后我们证明了Blok和Pigozzi在我们的环境中的同构定理的一种版本。我们将此框架应用于团队语义中的逻辑，并表明，好奇心和依赖逻辑的经典版本严格来说是可代数的，而其直觉版本只是零散的。
We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we introduce a loose and strict version of algebraizability for weak logics. We study this framework by investigating the connection between the algebraizability of a weak logic and the algebraizability of its schematic fragment, and we then prove a version of Blok and Pigozzi's Isomorphism Theorem in our setting. We apply this framework to logics in team semantics and show that the classical versions of inquisitive and dependence logic are strictly algebraizable, while their intuitionistic versions are only loosely so.
