Inverse rule

Paul Lorenzen and other logicians use the term logical inversion to describe the process of reversing a rule of calculus .

Let be a valid rule of a calculus: ${\displaystyle R}$

${\displaystyle P\Rightarrow K}$.

Here is the premise and the conclusion of . Then the inverse rule is: ${\displaystyle P}$ ${\displaystyle K}$ ${\displaystyle R}$

${\displaystyle K\Rightarrow P}$.

The inverse of a valid rule is, of course, generally not one that is valid in the calculus; H. deducible rule; this must first be proven in individual cases.

literature

• Hans Hermes: Introduction to mathematical logic: classical predicate logic , 4th A. 1976, p. 56.