The Logic package uses a two-valued logic system, while standard Maple logic is three-valued.  For this reason, all Boolean expressions used in the Logic package must be expressed in terms of the operators &and, &iff, &implies, &nand, &nor, &not, &or, and &xor.

You may either enter expressions in terms of these operators directly into Maple, or transform expressions of type logical into expressions in terms of these operators with the Logic[Import] command.

Note that the Logic package operators do not have the same precedence as corresponding three-valued operators.  In particular, all operators have the same precedence, so $a\&\mathbf{or}b\&\mathbf{and}c$ is equivalent to $\left(a\&orb\right)\&andc$, not $a\&or\left(b\&andc\right)$. Parentheses should be used to correctly specify the precedence.

$\mathrm{with}\left(\mathrm{Logic}\right)\:$

$\mathrm{Export}\left(a\&orb\,\mathrm{form}=\mathrm{MOD2}\right)$

$1+\left(a+1\right)\left(b+1\right)$

$\mathrm{Export}\left(\left(\left(a\&norb\right)\&andc\right)\&orb\right)$

$\mathbf{not}\left(a\mathbf{or}b\right)\mathbf{and}c\mathbf{or}b$

$\mathrm{Import}\left(a\Rightarrow b\mathbf{or}c\right)$

$a\Rightarrow \left(b\vee c\right)$

$\mathrm{Export}\left(\left(\left(\left(\&not\left(a\right)\right)\&orb\right)\&xorc\right)\&nandb\,\mathrm{form}=\mathrm{boolean}\right)$

$\mathbf{not}\left(\left(\mathbf{not}a\mathbf{or}b\mathbf{xor}c\right)\mathbf{and}b\right)$