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The phrase "as a causal process" is correct and usable in written English.
It can be used in contexts discussing the nature of events or phenomena that occur as a result of specific causes.
Example: "The researchers examined the phenomenon as a causal process to understand the underlying mechanisms at play."
Alternatives: "as a result of causation" or "in terms of cause and effect".
Exact(3)
Inner sense accounts' construal of introspection as a causal process makes them particularly well-suited to reliabilist (or, more broadly, epistemically externalist) approaches to self-knowledge.
Based on the unscented Kalman filter, Malcolm et al. presented a filtering strategy that treats model estimation and tractography as a causal process [43, 44].
Hume describes their operation as a causal process: custom or habit is the cause of the particular propensity you form after your repeated experiences of the constant conjunction of smoke and fire.
Similar(57)
So while mark transmission may well be a criterion that correctly distinguishes between causal processes and pseudo-processes, it does not, as it stands, provide the resources for distinguishing those features or properties of a causal process that are causally or explanatorily relevant to an outcome and those features that are irrelevant.
Our findings support the hypothesis that CA frequency, although indirectly measured in surrogate tissues, can predict the risk of cancer by itself as a phenotypic manifestation of multiple carcinogenic processes or as an intermediate step of a causal process.
In this new theory which is influenced by the conserved process theory of causation of Dowe (Dowe, 2000), Salmon defined a causal process as a process that transmits a non-zero amount of a conserved quantity at each moment in its history.
To begin with, a process may be a causal process even if it does not in fact transmit any mark, as long as it is true that if it were appropriately marked, it would transmit the mark.
Such an inference — as opposed to an "inference in itself" or an argument — is a causal process, to be clear.
The reason is a causal process.
Natural selection is a causal process.
Then a causal process is the world line of a causal object).
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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