The phrase "a matter of inference" is correct and usable in written English.
You can use it when discussing conclusions or deductions that are drawn from evidence or reasoning rather than from explicit statements.
Example: "The results of the experiment suggest that the observed behavior is a matter of inference rather than direct observation."
Alternatives: "a question of deduction" or "a case of reasoning".
It's a matter of inference, not just to any old explanation, but inference to the best explanation.
Often crimes are a matter of inference deduced from the acts of the person accused and done in pursuance of a criminal purpose.
Like any number of small- and big-screen thrillers, the film's engagement with 9/11 is diffuse, more a matter of inference and ideas (chaos, fear, death) than of direct assertion.
With this point established, "the connection of the defendants with the plan can be largely a matter of inference, with the burden on highly placed individuals in effect to disprove their connection with it" (p.4).
A second approach is to view that inductive step as a matter of inference to the best explanation, and this is a more promising possibility.
Moreover, the category of conventional implicatures blurs the distinction between what is said, usually conceived as determined by the semantic conventions of language, and what is implicated, usually thought of as a matter of inference as to a speaker's intentions in saying what she does.
The size of the sum can only be explained by an assumption that the businessman was going to get something of great value – something which, as a matter of obvious inference, could not be obtained by approaching Prince Andrew through proper channels.
We can think of this as a matter of the inference patterns to be sanctioned by some proof system offered for L, or as a matter of how the formulas of this language are to be interpreted by assigning suitable semantic values to them (truth-values being the simplest candidates here).
(Plato appears to think that plants do have minds in this sense, because he takes them to exhibit desire and sense-perception (Timaeus 77b), but that is presumably supposed to be a matter of empirical fact or inference, rather than simply a consequence of the fact that plants have souls).
An employee "has carried out his burden if he proves that he has in fact performed work for which he was improperly compensated and if he produces sufficient evidence to show the amount and extent of that work as a matter of just and reasonable inference," Kennedy wrote, citing a 70-year-old precedent that allowed for similar calculations for unpaid wages.
The court held that petitioner had failed to meet his burden because his allegations were insufficient as a matter of law to raise an inference of discrimination.
