摘要
通过推广de Rijke(1995)和van Benthem(2007)关于命题模态逻辑的Lind-ström定理结论,本文给出了一阶模态逻辑(∃)(□)-打包片段的三种不同的Lindström定理表述.三种表述均基于(∃)(□)-打包片段的互模拟不变性,此外,它们还分别利用了该片段的紧致性、有穷深度性以及自然数集上的超积不变性.
Abstract
In this paper,we provide three different Lindström theorems for(∃)(□)-bundled frag-ment of first-order modal logic,by generalizing de Rijke's(1995)and van Benthem's(2007)results for propositional modal logic.All three results are based on the property of bisimulation invariance,and each of them employs another property:compactness,finite depth property,and preservation under ultraproducts over the natural numbers,respectively.
基金项目
Fundamental Research Funds for the Central Universities(2023QNTS72)
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