TY - JOUR
AU - Francez, Nissim
PY - 2019
TI - Another plan for negation
JF - The Australasian Journal of Logic; Vol 16 No 5 (2019): The Australasian Journal of Logic
DO - 10.26686/ajl.v16i5.5190
KW -
N2 - The paper presents a plan for negation, proposing a paradigm shift from the Australian plan for negation, leading to a family of contra-classical logics. The two main ideas are the following: Instead of shifting points of evaluation (in a frame), shift the evaluated formula. Introduce an incompatibility set for every atomic formula, extended to any compound formula, and impose the condition on valuations that a formula evaluates to true iff all the formulas in its incompatibility set evaluate to false. Thus, atomic sentences are not independent in their truth-values. The resulting negation, in addition to excluding the negated formula, provides a positive alternative to the negated formula. I also present a sound and complete natural deduction proof systems for those logics. In addition, the kind of negation considered in this paper is shown to provide an innovative notion of grounding negation.
UR - https://ojs.victoria.ac.nz/ajl/article/view/5190