Journal of Philosophical Logic ( IF 0.7 ) Pub Date : 2021-11-20 , DOI: 10.1007/s10992-021-09634-4 Roy T. Cook 1
This essay introduces a novel framework to studying many-valued logics – the movable truth value (or MTV) approach. After setting up the framework, we will show that a vast number of many-valued logics, and in particular many-valued logics that have previously been given very different kinds of semantics, including C, K3, LP, ST, TS, RMfde, and FDE, can all be unified within the MTV-logic approach. This alone is notable, since until now RMfde in particular has resisted attempts to provide it with the same kind of many-valued semantics as the other logics in this list. New proofs of the duality between LP and K3, and of the self-duality of C, ST, TS, and RMfde, are presented. The essay will conclude with a discussion of directions that further research might take.
中文翻译:
MTV逻辑
本文介绍了一个研究多值逻辑的新框架——可移动真值(或MTV)方法。建立框架后,我们将展示大量的多值逻辑,尤其是之前被赋予了非常不同种类语义的多值逻辑,包括C、K3、LP、ST、TS、 RM fde和FDE,都可以在MTV逻辑方法中统一。仅这一点就值得注意,因为直到现在 RM fde特别抵制尝试为其提供相同类型的多值语义作为此列表中的其他逻辑。提出了LP和K3之间的对偶性以及C、ST、TS和 RM fde的自对偶性的新证明。本文将以讨论进一步研究可能采取的方向结束。