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It depends on how you use the word.

Logic in it's pure form would be a branch of mathematics, statistics, or informatics... and thus would be a science.

It may also be in the realm of philosophy that borders between arts and sciences.

However, it is also often used much less formally as in the phrase "That just seemed logical"... or "The logical conclusion was".... It may just describe a gut feeling... and not true science at all.

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Neither, logic is philosophy

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