I am teaching in an Eastern Asian environment (precisely, teaching Mathematics using English in Korea, with Asian students) and I figured out that my reasoning is a lot based on my language proficiency in English and latin languages. As a latin languages speaker, mistakes in the difference between definite article “the” and indefinite article “a” hurt me a lot, whereas these articles do not exist in my students' mother language (at least, in Korean). I also have a quite efficient writing style for proofs, organizing my reasoning on the multiple logical connectors that Western Europe languages provide: so, then, hence, therefore, as a consequence,...; the actual content of my sentences being as simple as possible to convey the mathematical content in the most straightforward way. More elaborated sentences are used for broad introduction of ideas, and conclusions. But other languages have a completely different structure.
I would be interested in references on how the structure of a language influences the logical reasoning. For example, I believe that the importance given on existence problems and unicity problems is mostly due to the emphasis on definite and indefinite articles in Western languages. When introducing a new mathematical object in class, I feel very uncomfortable having to say “a” until unicity is proved. For practical reasons, I am mostly interested in Asian languages (mainly Korean, and also Chinese and Japanese), but references for other languages may also be useful.