瞬时邻域逻辑的Sahlqvist对应理论
Sahlqvist Correspondence Theory for Instantial Neighbourhood Logic
摘要：
在本文中，我们研究的Sahlqvist型对应理论的实例邻域逻辑（INL），它可以谈论一个给定的世界的邻域的存在性信息，是一个关系语义和邻域语义之间的混合。我们对对应结果给出了两个证明，第一个证明是直接利用标准平移和最小赋值技术得到的，第二个证明遵循[4]和[6]，其中我们利用双峰平移方法将实例邻域逻辑中的对应问题约化为经典Kripke语义中的正常双峰逻辑。最后，我们给出了一些评论和未来的发展方向。
英文摘要：
In the present paper, we investigate the Sahlqvist-type correspondence theory for instantial neighbourhood logic (INL), which can talk about existential information about the neighbourhoods of a given world and is a mixture between relational semantics and neighbourhood semantics. We have two proofs of the correspondence results, the first proof is obtained by using standard translation and minimal valuation techniques directly, the second proof follows [4] and [6], where we use bimodal translation method to reduce the correspondence problem in instantial neighbourhood logic to normal bimodal logics in classical Kripke semantics. We give some remarks and future directions at the end of the paper.
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