论文标题
普世模态逻辑
Ecumenical modal logic
论文作者
论文摘要
关于如何在单个统一系统中建立古老的古典和直觉逻辑系统的讨论又重新恢复了时尚。确实，最近，普拉维兹（Prawitz）和其他人一直在讨论所谓的普世系统，这些逻辑中的连接可以和平共存。在Prawitz的系统中，古典逻辑学家和直觉逻辑学家将共享荒谬的通用量词，结合，否定和常数，但它们每个人都会具有不同的含义。 Prawitz的主要思想是，这些不同的含义是由双方都可以接受的语义框架给出的。在最近的一项工作中，提出了普世的序列结石和嵌套系统，并建立了一些非常有趣的证明理论特性。在这项工作中，我们将Prawitz的普遍构想扩展到了Alethic k模式。
The discussion about how to put together Gentzen's systems for classical and intuitionistic logic in a single unified system is back in fashion. Indeed, recently Prawitz and others have been discussing the so called Ecumenical Systems, where connectives from these logics can co-exist in peace. In Prawitz' system, the classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation, and the constant for the absurd, but they would each have their own existential quantifier, disjunction, and implication, with different meanings. Prawitz' main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. In a recent work, Ecumenical sequent calculi and a nested system were presented, and some very interesting proof theoretical properties of the systems were established. In this work we extend Prawitz' Ecumenical idea to alethic K-modalities.
