文章基本信息

标题：Consistency and Decidability in Some Paraconsistent Arithmetics
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作者：Andrew Tedder
期刊名称：Australasian Journal of Logic
印刷版ISSN：1448-5052
电子版ISSN：1448-5052
出版年度：2021
卷号：18
期号：5
DOI：10.26686/ajl.v18i5.6921
语种：English
出版社：Philosophy Department, University of Melbourne
摘要：The standard style of argument used to prove that a theory is unde- cidable relies on certain consistency assumptions, usually that some fragment or other is negation consistent. In a non-paraconsistent set- ting, this amounts to an assumption that the theory is non-trivial, but these diverge when theories are couched in paraconsistent logics. Furthermore, there are general methods for constructing inconsistent models of arithmetic from consistent models, and the theories of such inconsistent models seem likely to differ in terms of complexity. In this paper, I begin to explore this terrain, working, particularly, in incon- sistent theories of arithmetic couched in three-valued paraconsistent logics which have strong (i.e. detaching) conditionals.