Minimal logic

Minimal logic, or minimal calculus, is a symbolic logic system originally developed by Ingebrigt Johansson. It is an intuitionistic and paraconsistent logic, that rejects both the law of the excluded middle as well as the principle of explosion (ex falso quodlibet), and therefore holding neither of the following two derivations as valid:

${\displaystyle \vdash (B\lor \neg B)}$

${\displaystyle (A\land \neg A)\vdash }$

where ${\displaystyle A}$ and ${\displaystyle B}$ are any propositions. Most constructive logics only reject the former, the law of excluded middle. In classical logic, also the ex falso law

${\displaystyle (A\land \neg A)\to B}$,

or equivalently ${\displaystyle \neg A\to (A\to B)}$, is valid. These do not automatically hold in minimal logic.

Note that the name minimal logic sometimes also been used to denote logic systems with a restricted number of connectives.