论文标题
关于中级理由逻辑
On Intermediate Justification Logics
论文作者
论文摘要
我们研究抽象的中间理由逻辑，即以（经典）理由逻辑的特定公理的子集扩展了任意的中间命题逻辑。为此，我们通过将Heyting代数或Kripke框架与Mkrtychev，Fitting或Lehmann's和Studer的经典合理性逻辑的模型相结合，从而介绍了各种语义。我们证明了使用基础中间逻辑的各个命题完整性定理的所有中间理由逻辑及其相应语义的统一完整定理。此外，通过修改拟合方法，我们证明了一类中间理由逻辑和随附的中间模态逻辑的统一实现定理。
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining either Heyting algebras or Kripke frames with the usual semantic machinery used by Mkrtychev's, Fitting's or Lehmann's and Studer's models for classical justification logics. We prove unified completeness theorems for all intermediate justification logics and their corresponding semantics using a respective propositional completeness theorem of the underlying intermediate logic. Further, by a modification of a method of Fitting, we prove unified realization theorems for a large class of intermediate justification logics and accompanying intermediate modal logics.
