Another plan for negation

Abstract

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: 

1. Instead of shifting points of evaluation (in a frame), shift the evaluated formula.
2. 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. 
3. The resulting negation, in addition to excluding the negated formula, provides a positive alternative
4. 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.