Another plan for negation
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.