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The phrase "ability to think logically" is correct and usable in written English.
You can use it when discussing someone's cognitive skills or reasoning capabilities.
Example: "In order to solve complex problems, one must possess the ability to think logically and critically."
Alternatives: "capacity for logical reasoning" or "skill in logical thought."
Exact(9)
"These [tests] are designed to measure your numeracy, spelling and ability to think logically".
"An ability to think logically, the ability to communicate ideas at different levels.
Patients suffering from aphasia may retain such intellectual powers as the ability to think logically, to plan and recollect.
Mr. Slavin's lawyer, Robert J. Del Col, argued in his opening statement that Mr. Slavin's tattoos were irrelevant and that the references to them were intended to muddle the jury's ability to think logically.
The Swiss psychologist Jean Piaget took the intellectual functioning of adults as the central phenomenon to be explained and wanted to know how an adult acquired the ability to think logically and to draw valid conclusions about the world from evidence.
The purpose of recent programming education is not to develop human resources who can write a program using a programming language but to gain 'computational thinking skills' (Papert 1980; Wing 2006), which would play an important role to learn science (Basu et al. 2016) and build an ability to think logically.
Similar(51)
"I have to think logically.
Again, this was out of sheer embarrassment and momentary incapacity to think logically.
What they're doing is helping kids to think for themselves, and to think logically, step-by-step.
The maths teacher told us that it taught us to think logically; to use a step-by-step approach in working through problems.
His reasoning, supported by many educators, is that in learning chess, children are taught to think logically, to plan and to use mathematics in a practical way.
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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