混合公开宣告逻辑

人类在思考问题时,常常伴随着对各种可能情形的审视。在经典公开宣告逻辑中,排除掉不可能的情形即实现对信念的修正。为了能够在语言中直接表达可能情形,本文探讨公开宣告逻辑的混合化,即增加用于指称可能情形的专名。结合对直接和间接宣告的区分,引入三个不同的语言。公开宣告逻辑的混合化会导致技术上的困难,为防止专名失去指称,本文采取基于K45模型的“删链”语义学。在此基础上,本文考察宣告须真和宣告可假两种语义设定,共引入五个混合公开宣告逻辑,对比它们的表达能力,并给出可靠且完全的公理系统。

Hybrid Logic of Public Announcements

In this paper,we study the combination of hybrid logic and public announcement logic.We adopt the“link-cutting”semantics based on K45 models to prevent nominals from losing denotation.We investigate both classical and indirect public announcements in this new setting.We also consider logics with only truthful announcements and those allowing false ones.Five logics based on three languages interpreted over two semantics are introduced.Their relative expressivity results and sound and complete axiomatizations are studied in the paper.