The following logical query operators exist: $and, $or, and $nor. There also exists $not, however this is a field-level operator, while the aforementioned are not field-specific.

I propose the introduction of a $nand operator as a compliment to $and, $or, and $nor.

Given the following query:

{
	$and: [
		{a: 1},
		{b: 2}
	]
}

The current way to implement NAND logic:

{
	$or: [
		{'a': { $ne: 1} },
		{'b': { $ne: 2} }
	]
}

This is problematic when an existing complex query exists (read: nested operators, mixed notation, etc.) and must be transformed. Before sending the query to MongoDB, it would have to be interpreted and the $ne operator strategically placed. It would be easier and less error-prone to use the existing query and wrap it in a $nand:

{
	$nand: [
		{a: 1},
		{b: 2}
	]
}

Existing use cases are on Google Groups and StackOverflow.