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The phrase "a relation of satisfaction" is correct and usable in written English.
It can be used in contexts discussing the connection or association between entities that leads to a sense of fulfillment or contentment.
Example: "In the study of consumer behavior, researchers often explore a relation of satisfaction between product quality and customer loyalty."
Alternatives: "a connection of satisfaction" or "a link of satisfaction".
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Tarski defined truth for formal (logical or mathematical) languages in terms of a relation of "satisfaction" between the constituents of a sentence and sequences of objects.
We now define a relation of satisfaction between interpretations, variable-assignments, and formulas of L1K=.
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The use of the relation of satisfaction, or being-a-model-of, between a structure and a theory (or a sentence) can be traced to the book Wissenschaftslehre (1837; Theory of Science) by Bernhard Bolzano, a Bohemian theologian and mathematician, and, in a more concrete context, to the introduction of models of non-Euclidean geometries about that time.
Tarski notes that the relation of satisfaction and a truth predicate for LGTC (and LGTC+) are definable in these more powerful metatheories (cf. Tarski 1983b, pp. 271 2).
In particular, the relation of satisfaction for LCC is a relation that can be found in the hierarchy of finite types.
The relation of satisfaction for LGTC is intuitively a relation among formulae and sequences of: sequences of individuals, sequences of classes of individuals, sequences of classes of classes of individuals, etc.
Pilar was a relation of theirs.
A Swedish study of 36 patients with a carcinoid tumour showed a positive relation between satisfaction with doctors' provision of information and emotional function and global QoL at three of the four time points [ 12].
However, a study of 36 carcinoid tumour patients found a negative relation between satisfaction with doctors' provision of information and anxiety and depression at the first three of four time points (T1 T3) [ 12].
"There's a feeling of satisfaction.
Did I detect a sense of satisfaction?
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com