I am using the term "predication" in the sense of "assertion" but not an assertion of truth. I spend time in both of my books on this defining this term. So for example, "the old man" taken as a phrase has three predications (that you would see in graphing it). These would be 'there is a man', 'the man is old', 'it is a specific man'. The truth of all three is presupposed. It is assumed in assertion. If you put it in a sentence as in "the old man jumped" then you get a fourth predication 'the old man jumped'. This would asserts the truth. If it is not factually true or has a deceitful motivation it can be a lie. The science says that truth itself is simply another predication. So each of the four above predications can be (independently) seen as a truth or lie. Where lie mean either factually untrue or true with a deceit that it is true or untrue, or a deceit that the motivation for the assertion was a deceit or not.

All of these meanings are available in established literatures associated with formal linguistics. But most important, they are not new. I just gave you the formal definition that anyone can confirm for themselves as is done in formal linguistics.

That said, no verbal description of anything cannot be misunderstood. Ever. That is the whole topic of my first paper on this subject on Medium, after publishing the two books. Here is that first paper 2.5 years ago.

I did appreciate that you were taking a different 'meaning' of "predication" by which I mean you were identifying in your brain a different collection of predications that were true about that word's sense. However anyone's brain is miraculously capable of adjusting predications about assertions (predications about other predications). This was the topic of that short paper you just read on "uniquely human". If you read it again you will see that is precisely the topic of that paper with this, admittedly technical, definition of "predication."

Note the use of single ' and double " reflecting the accepted difference between a 'sense of something' and "the literal thing". In the literature this is often the difference between deep and shallow, or somewhat oddly, shallow and deep. Different 'stratificational' systems make different assumptions. Modern NLP usually works with word senses (shallow) and establishes only the surface grammatical form embedding of propositions of word sense predications that you graph in high school. Newer and older NLP systems approach the deeper, purely conceptual systems that include predications of truth, deceit, and motivation.

Hope this helps. None of this is my own definition but admittedly I spent many years of my Ph.D. (badly non-social) life on formal linguistics and computational cognitive neuroscience on how the human brain computes verbal behavior.

It used to be called, experimental psychology of verbal learning and memory, later experimental cognitive psychology, then psycholinguistics, then cognitive science, then cognitive neuroscience, then computational cognitive science, then computational cognitive neuroscience. My first published paper was on experiments showing how verbal labels could interfere with or enhance visual memory in 1973.

But, I do use the sense of "predication" which is defined as "assertion". You wanted, I think, to take the meaning of it as a "sentence assertion" which is often composed of many assertions hierarchically embedded some of which have different assertions of truth, deceit, and motivation. My dissertation was on how sentences could be joined with independent and dependent clauses which are themselves sentences, and memory for such relations between sentences/clauses whether explicit inside of sentences with asserted predications of conjunction, or inferred between sentences. As in narratives or systems of anaphoric ('pronoun') reference.

Here is that first article where I define these in fewer words...but emphasizing the importance of understanding how the brain computes truth or lies.

https-medium-com-rhtcmu-fiat-lies-are-genocide-on-the-human-race-a4d76b093530