标题： 通过翻译的萨尔qvist 显示英文标题

标题： Sahlqvist via Translation

摘要： 近年来，统一对应性已被发展为一种广义的Sahlqvist理论，该理论适用于所有正则（分配）格扩张的符号集。这包括在每个这样的符号集中对Sahlqvist公式和归纳公式及不等式的普遍定义，该定义基于序理论。该定义特别涵盖了所有（双）直觉主义模态逻辑。这些逻辑的理论在过去七十年中被深入研究，与经典多词元模态逻辑相关，使用适当的Godel-McKinsey-Tarski翻译版本作为主要工具。因此，自然地会提出以下问题：(1) 是否可以基于类似于Sahlqvist和归纳公式及不等式普遍定义所依据的序理论原理，获得对Godel-McKinsey-Tarski翻译的普遍视角，该视角能够解释已知的Godel-McKinsey-Tarski翻译，并适用于所有正则（分配）格扩张的符号集；(2) 这种普遍视角是否可用于将Sahlqvist和归纳公式及不等式的对应定理和正规性定理，在上述所有符号集下的Godel-McKinsey-Tarski翻译中进行传递。在本文中，我们旨在回答这些问题。我们对(1)给出了肯定的回答；至于(2)，我们证明了任意正则分配格扩张符号集下归纳不等式的对应定理的传递性。我们还证明了归纳不等式的正规性传递性，但仅限于双直觉主义逻辑的任意正则模态扩张。我们还分析了在该设定之外获得正规性传递性所涉及的困难，并指出了将正规性传递性扩展到所有正则分配格扩张符号集的途径。 显示英文摘要

摘要： In recent years, unified correspondence has been developed as a generalized Sahlqvist theory which applies uniformly to all signatures of normal and regular (distributive) lattice expansions. This includes a general definition of the Sahlqvist and inductive formulas and inequalities in every such signature, based on order theory. This definition covers in particular all (bi-)intuitionistic modal logics. The theory of these logics has been intensively studied over the past seventy years in connection with classical polyadic modal logics, using suitable versions of Goedel-McKinsey-Tarski translations as main tools. It is therefore natural to ask (1) whether a general perspective on Goedel-McKinsey-Tarski translations can be attained, also based on order-theoretic principles like those underlying the general definition of Sahlqvist and inductive formulas and inequalities, which accounts for the known Goedel-McKinsey-Tarski translations and applies uniformly to all signatures of normal (distributive) lattice expansions; (2) whether this general perspective can be used to transfer correspondence and canonicity theorems for Sahlqvist and inductive formulas and inequalities in all signatures described above under Goedel-McKinsey-Tarski translations. In the present paper, we set out to answer these questions. We answer (1) in the affirmative; as to (2), we prove the transfer of the correspondence theorem for inductive inequalities of arbitrary signatures of normal distributive lattice expansions. We also prove the transfer of canonicity for inductive inequalities, but only restricted to arbitrary normal modal expansions of bi-intuitionistic logic. We also analyze the difficulties involved in obtaining the transfer of canonicity outside this setting, and indicate a route to extend the transfer of canonicity to all signatures of normal distributive lattice expansions.