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: 
 
 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.