boolean.json

( (1 or 2 or 3) and (not (4 and (5 or 6 ) ) ) )

{
	"operator": "AND",
	"subsections": [
		{
			"operator": "OR",
			"entities": [ 1, 2, 3 ]
		},
		{
			"operator": "NOT",
			"subsections": [
				{
					"operator": "AND",
					"subsections": [
						{
							"operator": "OR",
							"entities": [ 4 ]
						},
						{
							"operator": "OR",
							"entities": [ 5, 6 ]
						}
					]
				}
			]
		}
	]
}

Arguably human-friendly JSON proposal: https://github.com/MediaMath/nemo/blob/qa/docs/endpoints.md