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Noun rigour has 3 senses
cogency, validity, rigor, rigour - the quality of being logically valid--1 is a kind of credibility, credibleness, believability
 
asperity, grimness, hardship, rigor, rigour, severity, rigorousness - something hard to endure; "the asperity of northern winters"--2 is a kind of difficulty, difficultness
 
severity, harshness, rigor, rigour, inclemency, hardness, stiffness - excessive sternness; "severity of character"; "the harshness of his punishment was inhuman"; "the rigors of boot camp"--3 is a kind of sternness, strictness
 
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