Consistency and Decidability in Some Paraconsistent Arithmetics

Andrew Tedder
2021 The Australasian Journal of Logic  
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
more » ... dels 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.
doi:10.26686/ajl.v18i5.6921 fatcat:ylxgkhrmava2po7kybx53izclq