Liberman等人（2020）针对带等词与非刚性项的项模态逻辑K所提出的希尔伯特式系统的语义不完备性
Semantic Incompleteness of Liberman et al. (2020)'s Hilbert-style System for Term-modal Logic K with Equality and Non-rigid Terms
AI总结：
本文证明Liberman等人（2020）针对带等词与非刚性项的项模态逻辑K提出的希尔伯特式系统语义不完备，并通过引入使常元和函数符号含义相对化的非标准克里普克语义给出反例。
摘要：
本文证明了Liberman等人（2020）在《用于一阶认知规划的动态项模态逻辑》中提出的、针对带等词和非刚性项的最小正规项模态逻辑的希尔伯特式系统的语义不完备性。项模态逻辑是一族一阶模态逻辑，其一阶语言中的项被用作项模态算子的索引。虽然在该文所提出的项模态逻辑克里普克语义下，某个一阶公式在所有框架类上都是有效的，但它在Liberman等人（2020）的希尔伯特式系统中不可推导。我们通过引入一种非标准克里普克语义来展示这一事实，该语义使常元和函数符号的含义相对于与它们结合的关系符号的含义而变化。
英文摘要：
In this paper, we prove the semantic incompleteness of the Hilbert-style system for the minimal normal term-modal logic with equality and non-rigid terms that was proposed in Liberman et al. (2020) "Dynamic Term-modal Logics for First-order Epistemic Planning." Term-modal logic is a family of first-order modal logics having term-modal operators indexed with terms in the first-order language. While some first-order formula is valid over the class of all frames in the Kripke semantics for the term-modal logic proposed there, it is not derivable in Liberman et al. (2020)'s Hilbert-style system. We show this fact by introducing a non-standard Kripke semantics which makes the meanings of constants and function symbols relative to the meanings of relation symbols combined with them.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
