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史 and its associated characters

又 [hand (original meaning), again]

史 [history]

吏 [government official]

使 [cause, use, instruct]

事 [matter, work, affair] 

邏輯 [logic] a loanword (19th Century, late 清 Qing) from Greek λογική (the specific philosophical study of reasoning) or λόγος (which encompasses a broader semantic range). The English word "logic" also derives from Greek.

Of course, this doesn't mean Chinese (or English) did not have a word for similar concepts to logic before「邏輯」or "logic". English, for example, used words like "reason", "sophistry" to mean similar things. Chinese would use words like 道理 [reason] or 理性 [rationality].