The Proto-Indo-European root "to know" is *ǵneh₃-. It also lends itself to the Greek word "gnosis", which itself has a contested meaning. The philosophy of knowledge, epistemology, is Greek for "logical discourse of knowledge". "Knowledge" is "episteme", "logic" is "logos", and Discourse is the software this forum uses.
However, neither episteme nor logos seem related to our modern definitions of knowledge or logic. Episteme comes from Proto-Indo-European *h₁epi, which means "on, at, near", and *steh₂, which means to "to stand". Proto-Indo-European *leǵ-, the root of both logos and Latin "lego", simply means "to gather". Curiously enough, lego means "to put together". Perhaps why Legos are thusly named?
In short, epistemology seems only to mean "standing on what is gathered" at its most ancient known roots. Very different from either logic, knowledge, or gnosis, at least with their current conventional meanings. I suppose it isn't so different though. Maybe knowledge is our perception of the world, the foundation our beliefs and actions "stand upon", formed through both experience and intuition, what we "gather".
When I say I only know something to "the best of my knowledge", my knowledge is simply an educated guess from my own personal "School Of Life". I could be wrong, but there is usually some truth in what I say, because there is truth in everything. The concept or "right" and "wrong" is simply a spectrum. When I tell my boyfriend "I gather you'll make yourself sick eating that whole cake", that means I have "gathered" information and can make another educated guess. "Standing by (near/at/on) what I say" means basing my decisions in that perception.
I'm not really sure what my point is. So many words have debatable definitions, including half the words in this past paragraph. The study of linguistics is a fascinating topic though, and so many terms have roots that may seem the total opposite. For example, "whore" comes from Proto-Indo-European *keh₂ro-, meaning "dear" or "loved". A far cry from "slut". Although *keh₂ro- comes from *keh₂-, "desire" or "wish". More debatable words.