On axiomatizations of public announcement logic
On axiomatizations of public announcement logic
复制标题
论公告逻辑的公理化
DOI：
10.1007/s11229-012-0233-5
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发表时间：
2013
期刊：
影响因子：
1.5
通讯作者：
Qinxiang Cao
中科院分区：
文献类型：
--
作者：
Yanjing Wang;Qinxiang Cao
在文献中，已经提出了公告逻辑（PAL）的不同公理化。这些公理化中的大多数都有一个所谓的“还原公理”的“核心集”。本文通过为pal语言设计非标准的Kripke语义，证明了在没有附加公理和规则的情况下，基于该核心公理集的证明系统不能完全公理化pal。事实上，我们认为理所当然的许多直观公理和规则都不能从核心集合中推导出来。此外，我们还提出并提倡一种替代的但有意义的无约化公理的pal公理化。完备性通过使用规范模型的绕行方法直接证明，在规范模型中，公告仅仅被视为模态的标签，就像在正常模态逻辑中一样。这种新的公理化及其完备性证明可以加深我们对pala的认识，并适用于其他动态认知逻辑。
In the literature, different axiomatizations of Public Announcement Logic (PAL) have been proposed. Most of these axiomatizations share a “core set” of the so-called “reduction axioms”. In this paper, by designing non-standard Kripke semantics for the language ofPAL, we show that the proof system based on this core set of axioms does not completely axiomatizePALwithout additional axioms and rules. In fact, many of the intuitive axioms and rules we took for granted could not be derived from the core set. Moreover, we also propose and advocate an alternative yet meaningful axiomatization ofPALwithout the reduction axioms. The completeness is proved directly by a detour method using the canonical model where announcements are treated as merely labels for modalities as in normal modal logics. This new axiomatization and its completeness proof may sharpen our understanding ofPALand can be adapted to other dynamic epistemic logics.