Another plan for negation

  • Nissim Francez Technion-IIT


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. 


Author Biography

Nissim Francez, Technion-IIT
Logic (in particular proof theory) and natural language semantics
How to Cite
FRANCEZ, Nissim. Another plan for negation. The Australasian Journal of Logic, [S.l.], v. 16, n. 5, p. 159-176, aug. 2019. ISSN 1448-5052. Available at: <>. Date accessed: 23 sep. 2019. doi: