The phrase "logically rigorous" is correct and usable in written English.
It can be used to describe a process, argument, line of reasoning, etc. that has been done in an organized, logical, and precise manner. For example: "The author's argument was carefully constructed, making it logically rigorous and helping to create a convincing case."
Inspired by the work of the mathematicians whom he so greatly admired, Russell conceived the idea of demonstrating that mathematics not only had logically rigorous foundations but also that it was in its entirety nothing but logic.
In retrospect, these and other theories seem to have been neither logically rigorous nor able to account for both intellectual and emotional growth within the same framework.
A much greater influence on his thought at this time, however, was a group of German mathematicians that included Karl Weierstrass, Georg Cantor, and Richard Dedekind, whose work was aimed at providing mathematics with a set of logically rigorous foundations.
Philosophically inclined thinkers have both historically and at present labored to shape the relevant intuition into a more formal, logically rigorous inference.
Rather than seek to formulate an elaborate intellectual argument whose parts were integrated into a logically rigorous analysis, Obama chose to present a sort of collage or, perhaps more accurately, a modernistic painting a la Kandinsky.
Mark Skousen of Grantham University and the Foundation for Economic Education, a critic of mainstream economics, praises Rothbard as brilliant, his writing style persuasive, his economic arguments nuanced and logically rigorous, and his Misesian methodology sound.
He intends (1) to determine the ontological status and nature of the complexe significabile more precisely; and (2) to develop a general theory of the proposition which would be logically more rigorous and less compromised by a metaphysics of the possible than that supported by Gregory of Rimini, his main source on that subject.
The in-depth analysis and commentary of the literature that we perform here is meant to show that there is rigorous, logically compelling, and experimentally testable biological evidence for the usefulness of an aneuploid quasispecies theory.
This initiative was motivated by the fact that reporting results of forensic examinations in a logically correct and scientifically rigorous way is a daily challenge for any forensic practitioner.
Last but not the least, as mentioned earlier, the standard position of current studies on ontology is that the formal ontology is the rigorous and logically robust system which is the shared foundation of knowledge representation through either domain specific (and potentially inconsistent) local ontologies, as well as less rigorous and potentially conflicting language specific ontologies.
An op-ed that she recently wrote for the Los Angeles Times was more elaborate and confused: she now declares that her film is "rigorous" (historically rigorous? logically? morally?) and avows that she is a "lifelong pacifist" who supports "all protests against the use of torture".
