On Consistency and Decidability in Some Paraconsistent Arithmetics

0546146 - FLÚ 2022 RIV AU eng J - Journal Article
Tedder, Andrew
On Consistency and Decidability in Some Paraconsistent Arithmetics.
Australasian Journal of Logic. Roč. 18, č. 5 (2021), s. 473-502. E-ISSN 1448-5052
Institutional support: RVO:67985955
Keywords : Consistency * Decidability * Paraconsistent logics * Paraconssistent Arithmetics
OECD category: Philosophy, History and Philosophy of science and technology
Method of publishing: Open access
https://doi.org/10.26686/ajl.v18i5.6921

The standard style of argument used to prove that a theory is undecidable relies on certain consistency assumptions, usually that some fragment or other is negation consistent. In a non-paraconsistent setting, 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 inconsistent theories of arithmetic couched in three-valued paraconsistent logics which have strong (i.e. detaching) conditionals.
Permanent Link: http://hdl.handle.net/11104/0322697