Logical meaning of the word "understand"
Solution 1:
It's not "logical". It's metaphorical. Here's the etymology from the OED:
[OE. understondan, -standan (under-1 8 a), = OFris. understonda, MDa. understande, MSw. undi(r)standa, OIcel. (as a foreign word) undirstanda. Cf. MLG. understân to understand, to step under, MDutch onderstaen (Dutch -staan), MHG. understân, -stên (G. unterstehen), to take upon oneself, to venture, presume, etc.
With a different prefix, the same use of stand appears in OE. forstandan, OS. farstandan, OHG. far-, firstantan (firstân), and MHG. verstân, -stên (G. verstehen), MDutch verstaen (Dutch -staan). In the 15th and 16th cents. three forms of the past participle were current, viz. (a) the original understanden (also -stonden), in use till about 1550; (b) the reduced form of this, understande (-stonde), -stand (-stond), common till about 1575, and surviving into the 17th cent.; (c) the new form understanded (-stonded), very common from about 1530 to 1585. The occurrence of understanded in the Thirty-Nine Articles, xxxv, in the phrase `understanded of the people', has given rise to recent echoes of it, especially in journalistic use. The modern form understood came into use in the latter part of the 16th cent., and was usual by 1600. ]
So understand means to stand under (we would now say "stand behind" as a more common idiom), to know well, to have trust in, to have personal confidence in, etc. To say one understands a task, a trade, a fact, an idea, a job, the meaning of a word, or a person means all that. The personal aspect of the word is pre-eminent.
Solution 2:
You can't assume a current word superficially constructed from multiple elements which are also current words can necessarily be easily "deconstructed" from current meanings of the components.
From OED, it appears English imported understand wholesale from Middle Dutch onderstaen (to take upon oneself, to venture, presume). But Old English also had the same use of "stand" in forstandan.
From pp 210-214, An Analytic Dictionary of English Etymology, An Introduction (2008):
OE. forstandan, OHG firstantan, firstan 'verstehen' may have meant primarily 'stand before,' and hence 'watch, observe, perceive'. And just as the "stand" component semantically relates to perception, standpoint rather than physical posture, the "under" component is actually more among, within rather than beneath, supporting.
Be warned that if you follow the above link, you're looking at six pages of densely-packed analysis of the etymology of understand; attempts to summarise it here are somewhat futile.
I'm not sure any of this will really help OP. It just serves as a reminder that language evolves - things which look similar today may be unrelated, and things which look dissimilar may have a common origin.
Solution 3:
The prefix under in understand does not mean "beneath", but rather appears to be from an unrelated root mean "among". Allow me to quote etymonline.com:
O.E. understandan "comprehend, grasp the idea of," probably lit. "stand in the midst of," from under + standan "to stand" (see stand). If this is the meaning, the under is not the usual word meaning "beneath," but from O.E. under, from PIE *nter- "between, among" (cf. Skt. antar "among, between," L. inter "between, among," Gk. entera "intestines;" see inter-).
That is the suggestion in Barnhart, but other sources regard the "among, between, before, in the presence of" sense of O.E. prefix and preposition under as other meanings of the same word. "Among" seems to be the sense in many O.E. compounds that resemble understand, e.g. underniman "to receive," undersecan "to investigate," underginnan "to begin." It also seems to be the sense still in expressions such as under such circumstances.
Perhaps the ultimate sense is "be close to," cf. Gk. epistamai "I know how, I know," lit. "I stand upon." Similar formations are found in O.Fris. (understonda), M.Dan. (understande), while other Germanic languages use compounds meaning "stand before" (cf. Ger. verstehen, represented in O.E. by forstanden). For this concept, most I.E. languages use figurative extensions of compounds that lit. mean "put together," or "separate," or "take, grasp" (see comprehend). O.E. oferstandan, M.E. overstonden, lit. "over-stand" seem to have been used only in literal senses.