论文标题
倾斜的分析归纳不平等的典范
Slanted canonicity of analytic inductive inequalities
论文作者
论文摘要
我们证明了一个代数的典范定理，用于正常的任意签名的正常LE逻辑，在广义的环境中，非晶格连接剂被解释为映射给定晶格的元素的操作，以映射给定晶格的元素，以构图其规范扩展的封闭或开放元素。有趣的是，在这种广义环境中保证其规范性的句法形状证明其符合分析归纳不平等的句法形状，这可以保证通过适当显示计算的分析结构规则来捕获Le-nequalities。我们表明，这种规范性结果连接并加强了许多近期的典型性结果，在两个不同的领域：从属代数，以及通过Gödel-Mckinsey-Tarski翻译转移结果。
We prove an algebraic canonicity theorem for normal LE-logics of arbitrary signature, in a generalized setting in which the non-lattice connectives are interpreted as operations mapping tuples of elements of the given lattice to closed or open elements of its canonical extension. Interestingly, the syntactic shape of LE-inequalities which guarantees their canonicity in this generalized setting turns out to coincide with the syntactic shape of analytic inductive inequalities, which guarantees LE-inequalities to be equivalently captured by analytic structural rules of a proper display calculus. We show that this canonicity result connects and strengthens a number of recent canonicity results in two different areas: subordination algebras, and transfer results via Gödel-McKinsey-Tarski translations.
