Title: Semantic Incompleteness of Liberman et al. (2020)'s Hilbert-style System for Term-modal Logic K with Equality and Non-rigid Terms Show Chinese title

Title: Liberman等（2020）的带有等式和非刚性项的术语模态逻辑K的希尔伯特风格系统的语义不完整性

Abstract: 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. Show Chinese abstract

Abstract: 在本文中，我们证明了Liberman等人在(2020)年提出的带有等式和非刚性项的最小正规项模态逻辑的希尔伯特系统语义不完全性。项模态逻辑是一类一阶模态逻辑，其具有由一阶语言中的项索引的项模态算子。虽然某些一阶公式在该文中提出的项模态逻辑的克里普克语义的所有框架类中有效，但它在Liberman等人(2020)的希尔伯特系统中不可推导。我们通过引入一种非标准的克里普克语义来证明这一事实，该语义使常量和函数符号的含义相对于与之结合的关系符号的含义而相对。