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.

Typing the Logic package operators: You must use 1-D math to enter these operators.

Precedence: 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 &or b &and c is equivalent to (a &or b) &and c, not a &or (b &and c). Parentheses should be used to correctly specify the precedence.

with(Logic):

Export(a &or b, form=MOD2);

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

Export((a &nor b &and c) &or b);

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

Import(a implies b or c);

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

Export((&not a &or b &xor c) &nand b, form=boolean);

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