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There is a solution to the word problem for finitely presented (non-bounded) lattices, as well as a solution to the word problem for free bounded lattices. I am assuming that there is a solution to the word problem for finitely presented bounded lattices, but so far I have been unable to find any literature on the topic. So has a solution to this word problem been found?

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    $\begingroup$ You can derive the bounded case from the unbounded case. $\endgroup$
    – Keith Kearnes
    Commented Nov 15, 2017 at 1:53

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