The phrase "a foundational problem in" is correct and usable in written English.
It can be used when discussing a core issue or challenge within a specific field or context.
Example: "The researchers identified a foundational problem in the current methodology that needs to be addressed for future studies."
Alternatives: "a fundamental issue in" or "a core challenge in".
In (Wallace 2006) unitarily inequivalent representations are not considered a foundational problem for QFT, while in (Ruetsche 2003) and (Kronz and Lupher 2005) unitarily inequivalent representations are considered physically significant.
These are fail-safe points in discussions of artistic freedom, and they sidestep a foundational problem: the decision to make art without regard for the lives involved, and no matter the consequences.
Hill (2004, p. 627, 628) argues that the concept of superaddition "is quite out of place" in connection with cohesion, because Locke regards cohesion as a foundational problem, which thwarts our efforts to conceive of body.
Rather, the point is that the MacCAT-T appears to be profoundly off the mark; that there is a foundational problem with the theory.
The groundwork was a study of the four foundational problems in axiomatic formulations of pure logic.
They continue to pose foundational problems in semantics and set theory.
Projective geometry has its own foundational problem, akin to that of distance in Euclidean geometry, which concerns the concept of cross-ratio, and we need to follow the moves to create projective geometry as an independent subject, to define cross-ratio in this setting, and to resolve the epistemological issues that are raised (an achievement associated with Klein's Erlangen Programme).
The fourth foundational problem, the decision problem for predicate logic, was shown to have a negative solution in a short paper by Church in 1936 as a corollary to Gödel's incompleteness theorem.
Yet, when we come to the most challenging and foundational problem of building autonomous agents capable of performing scene understanding in unrestricted videos, there is still a lot to be done.
