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直接自指的消除 (The Elimination of Direct Self Reference)

2022-08-29 17:19:04

主讲人:曽千里、熊明

会议链接:http://logic.fudan.edu.cn/event2022/acpomc#Program


摘要:This paper provides a procedure which from any Boolean system of sentences, outputs another Boolean system called the `m-cycle unwinding' of the original Boolean system for any positive integer m. We prove that for all m>1, this procedure eliminates the direct self-reference in the sense that the $m$-cycle unwinding of any Boolean system must be indirectly self-referential. More importantly, this procedure can preserve the primary periods of Boolean paradoxes: whenever m is relatively prime to all primary periods of a Boolean paradox, this paradox and its m-cycle unwinding have the same primary periods. In this way, we can always produce an indirectly self-referential Boolean paradox which has the same periodic characteristics as a known Boolean paradox.