Morph Query Builder is new in Logos 7.2 to the Cloud Feature Set (included with Logos Now membership).
What is it?
A “Morph Query” document is a new document type that can be found on the Documents menu. This document type specifies a query that is run against a new and improved morph search engine under the hood.
What is it for?
It’s a point-and-click user interface for building complex morph queries.
How does it work?
Each Morph Query document specifies a morphological query using a “grid” approach where each column is a word to find with characteristics of that word that you define. The document also specifies:
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A set of resources to search (eg, SBL Greek New Testament). For Beta 1, this is restricted to just the SBL Greek New Testament. Other resources should follow before launch.
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A search context that defines the possible extent of each search, which defaults to 10 segments. For now you can only set a different number of segments, but other result contexts such as verse and clause boundaries are anticipated. (If not by launch, soon thereafter.)
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A set of “constraints” that defines relationships between the terms in the query. For example, if two or more of the segments in the query must agree on case, number, and gender, that is defined as an agreement constraint on the query. If two or more of the segments must be within so many segments of one another, that is a proximity constraint. If two or more of the segments must appear in the results in the order they appear in the query, that is an ordering constraint. These constraints, along with “filtering” (see below) form the backbone of the improvements to the morph search engine.
The new morph search engine requires large databases, so it is an online service. Queries are constructed and saved locally as documents, which must contact the remote server via the Internet to execute the query and retrieve results, which are shown within the current Morph Search panel.
A new feature of the updated morph engine is “filtering,” that is, specifying segments that cannot exist within the search. Set the “Existence” row on any segment to “Does not exist” (defaults to “Exists”) and the entire potential result will be excluded.
Most properties can be given multiple values. You can read the query where each row implies “and” and each value within that row implies “or.” So in the example below, where “verb” is chosen in the “Part of Speech” row, and “participle, infinitive” are both chosen in the “Mood” row, you can read this as “a segment where the part of speech is verb AND the mood is participle or infinitive.”

Multiple columns can also be “merged” together to create alternation groups, that is, to match this segment or that segment.
For example, you could construct a query where there are three segments: Segment 1 is an article, Segment 3 is a ({noun, adjective, adverb} OR {verb, participle}) (ie, a substantive), and Segment 2 is a similarly-described substantive that appears between them in the query, but is marked as “Does not exist” meaning that it cannot appear between them in the result. Then if all three segments are constrained to agree on case, number, and gender, you end up with a query for finding articles (as defined by Segment 1) and following substantives (as defined by Segment 3) which they most likely modify (as defined by the agreement constraints), but with no other agreeing substantives in between (as defined by Segment 2). See figure below:

How do you use it?
Video: https://www.logos.com/logos-pro/morph-bible-search
Create a document that is then attached to an instance of the Morph Search panel. The document defines the search, and the Search panel shows the results.
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Go to Documents | New | Morph Query to create a new document.
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Specify your query in the document as described above. (It’s strongly suggested that you give it a name.)
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Open a Search panel and choose the Morph search type.
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Click on the down-pointing triangle at the left side of the morph input box (by launch this will be a grid-like icon) and choose the document you just made.

(Alternately, you can start from a Morph Search panel and choose Create morph query document from this menu to start the document from here. Then come back and do steps 2-4 with that newly created document.)
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The document is now attached, as evidenced by its name appearing in place of the text input control.
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Click on the document name to open the Morph Query document and edit it. (Edits are live, so you can make changes in the panel and then re-execute the query within the Morph Search panel as often as you need to.)
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Click the “x” after the document name to detach it and return to the normal morph text input control.
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Click right arrow in a circle icon at the far right of the same line of the Morph document to execute the search.