Just to clarify, the procedure I outlined above does allow emulation of NOT for tags. Which is to say, it does work and the logic can be expressed in various ways.
Yes, it’s messy and requires creation of some extra groups just to make it work. I would like to have the NOT operator available for tags, but in the interim I can use the kludge and obtain the same results in a couple of minutes or less. As I’ve needed this ability a couple of times, I used the kludge.
Here’s a stepwise variant that eliminates the deletion of replicants from a group (for those concerned about that).
- Using the full Search window for all searches in this procedure, do a search for the criteria other than tags that define the universe of items of interest.
Suppose, for example, that I’ve got a project involving literature that contains visions or projections about the future, especially about future science and technology.
That would include the broad category of what we call science fiction, as well as non-fictional extrapolations based on speculation about future developments in science and technology.
A) Polemical. Some of this literature emphasizes values, that is, a focus on whether human life would be better or worse as a result of a scientific or technological development. I might tag literature that sees positive impacts of science and technology as ‘utopian’ and literature that sees negative impacts as ‘dystopian’. For example, the speculative fiction of Edward Bellamy, e.g., Looking Backward, would be labelled as utopian. The speculative fiction of Aldous Huxley, e.g., Brave New World, and that of George Orwell, e.g., 1984, would be labelled as dystopian. Comment: Personally, I would view the utopia of Edward Bellamy as even more frightening and destructive of human values than the dystopia of George Orwell.
I’ll create a new Tags group called ‘Polemical’, with subgroups ‘Polemical utopia’, ‘Polemical dystopia’.
B) Projective: Some of this literature is primarily value-independent, projecting possible scientific and technological developments. That doesn’t mean that human values are totally removed in all cases, however.
For example, articles that appear frequently in scientific journals such as Science Magazine or Nature on topics such as future developments in the field of genomics often emphasize the potentials for diagnosis and control of diseases.
I would include in this category Vannevar Bush’s article, “As We May Think” and Ray Kurzweil’s book, The Singularity is Near.
I would include in this category many articles about genetic engineering of foods, that emphasize scientific information. But I would place others on that topic under the Polemical category instead.
I’ll create a Tags group named ‘Projective’ including as subgroups ‘Projective positive’, ‘Projective negative’, ‘Projective neutral’. I would tag Bush’s article as ‘Projective positive’. But one’s reaction to Kurzweil’s book might be more subjective and mixed. 
C) Entertaining: Most of this literature emphasizes entertainment of the reader as the primary purpose, whether or not values are noted in the content.
I would exclude Kurt Vonnegut’s “Harrison Bergeron” from this category and tag it as ‘Polemical dystopia’ instead. But I would include some other Vonnegut stories in category C.
Daniel Keyes’ “Flowers for Algernon” is one of my favorite science fiction stories and heavily emphasizes values. Nevertheless, I would include it in category 3. (This one emphasizes the difficulty of developing any rational tagging/categorizing scheme.)
Many SciFi stories - especially the pulp variety - are analogous to the old “cowboy and Indian” stores whose implicit values might be viewed differently, depending on whether one is a cowboy or an Indian.
I’ll create a Tags group called ‘Entertaining’ with subgroups ‘Entertaining positive’, ‘Entertaining negative’, ‘Entertaining neutral’.
To tag each item, I’ll ascribe it to one of the subgroups under each of my tag headings. Never tag an item with the top-level tag group, but only with a subgroup tag among these categories.
COMMENT: Are these sufficiently disjunctive and adequate categories and tags to describe a large body of literature? Certainly not, but suppose I’ve decided to use this simplistic and highly subjective system. Imagine that I’ve used the categories to define my groups and tags in a database and have applied them as consistently as I can.
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Suppose I’ve got all of Kurt Vonnegut’s writings concerning science and technology in my database and have tagged them according to the above scheme. Assume also that my database includes other items by or about Vonnegut, so that it includes items that were not tagged according to this scheme. Now I ask myself whether Vonnegut wrote anything that isn’t explicitly dystopian or negative about science and technology.
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First, I’ll do a search that will separate tagged and non-tagged items by or about Vonnegut. I’ll use the full Search window with its default settings, enter ‘Vonnegut’ as the query term and click on the ‘Advanced’ button.
Note that with my tagging system I could simply do a search for all items that have these tags: ‘Polemical utopian’ OR ‘Projective positive’ OR ‘Projective neutral’ OR ‘Entertaining positive’ OR ‘Entertaining neutral’. (To create multiple ‘OR’ statements for tags, hold the Option key when clicking on the “+” button to add a new predicate, select ‘Any’ instead of ‘All’ for the new item, then select ‘Tag’ and type the first letter of the new tag predicate and select the correct one.) (ASIDE: Note that if group tagging is enabled, this is a convenient way to create a smart group that lists the contents of multiple groups.)
The resulting list would show all the items that were tagged as Vonnegut writings that are non-pessimistic about science and technology.
But that search didn’t illustrate my technique for emulating a NOT operator for tags.
Let’s do that in the next step.
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Create a new group and name it ‘Vonnegut Non-Pessimistic Entertainment’. Select All the items in the above search results and replicate them to the group you just created.
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Open a new Search window. Click on the ‘Reset’ button if necessary, to reset the ‘Advanced’ button. Leave the query field blank. Click on ‘Advanced’ and enter a search that’s ‘Any’ (equivalent to the OR operator) for these multiple Tag predicates: ‘Polemical’ OR ‘Projective’.
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If there were any search results listed, create a new group and name it ‘Vonnegut Non-Pessimistic Polemical or Projective’. Select the search results from the Search window and move them to the new group. Now the results from the previous search results group are equivalent to having used a NOT operator for the last ‘Advanced’ search for tags. It contains only items having the ‘Entertaining’ tag.
Apologies for the long post, but I wanted to cover some of the difficulties and issues about classification/tagging, use of the full Search window and the Advanced button and use of the Option key when entering multiple predicates.
Bottom line: You can’t currently create a smart group that excludes a tag. But you can replicate the list of items in that smart group to a new group and in that group you can search for the items that contain one or more tags and move out those items from that group.
Note that when I use hierarchical tags (which can be tricky), I never tag items directly to the top level (but they will automatically be included there).
Caveat: I almost never tag new content as it is entered, as I think that’s entirely too much work. But when I’m working on a project, I may use tags to help me deal with the notes and documents used for that project – and often delete the tags when the project is completed.
