Duality

In propositional logic we say that two binary operations f and g are duals of one another if ¬f(α,β)=g(¬α,¬β).

If φ is a propositional formula, then φd, the dual of φ, is the result of replacing all occurrences of t with f and vice versa, and each occurrence of a binary connective with its dual.

Example

• Conjunction and disjunction are duals of one another: ¬(α∨β) = ¬α∧¬β

References

Fitting, Melvin. First-Order Logic and Automated Theorem Proving. Springer, 1990.