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. 



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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: 29 nov. 2020. doi: