# nLab weakening rule

The weakening rule

# The weakening rule

## Idea

In logic, the weakening rule states that premises may be added to the hypotheses of a valid deduction while remaining valid. Along with the contraction rule and the exchange rule, it is one of the most commonly adopted structural rules.

The weakening rule is not used in all logical frameworks, for instance in linear logic it is discarded.

## Statements

Exactly how this looks depends on the logic used.

## Semantics

This corresponds to having projections for the monoidal structure that corresponds to the logical binary operator at hand.

Last revised on October 4, 2022 at 11:27:06. See the history of this page for a list of all contributions to it.