A Completeness Proof for an Infinitary Tense Logic
A Completeness Proof for an Infinitary Tense Logic
复制标题
无限时态逻辑的完整性证明
DOI：
10.1111/j.1755-2567.1977.tb00778.x
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发表时间：
2008
期刊：
影响因子：
0.5
通讯作者：
G. Sundholm
中科院分区：
文献类型：
--
作者：
G. Sundholm
在他即将对G. H.冯赖特的时态逻辑[4]，克里斯特Segerberg研究了冯赖特创建的原始时态逻辑的某些无限扩展。对于其中一个扩展，完备性问题比乍看之下所预期的要难。本文致力于证明一个完整性定理的问题，称为Wl的Segerberg的扩展。我们使用普通命题逻辑的可数语言，提供两个模态运算符：O（“明天”）和D（“总是”）。基于这种语言的时态逻辑的相关语义使用框架9^ =，其中后继关系是O的可及性关系，并且n A在k处为真。我们假设读者熟悉模态语言的普通Kripkesemantics，特别是他理解“9 ft是框架9^上的模型”的含义。我将用它来做一个比喻。
In his forthcoming examination of G. H. von Wright's tense-logic [4], Krister Segerberg studies certain infinitary extensions of the original tense-logic created by von Wright. For one of these extensions the completeness problem turned out to be harder than was expected at first sight. This paper is devoted to a proof of a completeness theorem for the extension in question, called Wl by Segerberg. We use a countable language of ordinary prepositional logic supplied with two modal operators: O ("tomorrow") and D ("always"). The relevant semantics for tense-logic based on this language uses the frame 9^ = , where the successorrelation is the accessibility-relation for O and n A is true at k. We assume that the reader is familiar with ordinary Kripkesemantics for modal languages and, in particular, that he understands what it means that "9ft is a model on the frame 9^". We shall use O(A] as a shorthand for