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What is the difference between "tial" and "do"? What difference in meaning do the following two sentences have, if any? For example, in translating "My question is thus whether it is valid or not"...
”Tial” strictly refers back to a reason and is fairly uncommon, I’d say.
”Do” is a particle and is used in more contexts. According to PIV, it can express insisting when commanding something: ”Iru do!” and according to Revo surprise in a question ”Kie do li estas?”, Some people use ”do” like a filler word, like ”so” in English, when they don’t know what to say next.
”Do” can also mean ”therefore”, like in your example, but the usage in this case is somewhat broader than for ”tial”. Imagine you are approaching your teacher after Esperanto class saying ”Saluton, mi havas demandon.” Then you explain the context of the problem and finish with ”Mia demando tial/do estas...”. Now imagine instead that you intended to ask the question right away, but you got interrupted, or ran onto loads of sidetracks. In this case you would say ”Mia demando do estas...”. Here ”do” means something like ”pay attention” because you are entering the core of the conversation, or drawing a conclusion. PIV’s definition of this use is only in terms of ”logical consequence” while Revo defines it as ”Sekve de tio, konsekvence, konklude.”
There is a difference in meaning between the two words:
do indicates a logical consequence;
tial indicates a reason.
In your particular sentences this difference in meaning has essentially the same result: the reason why you are asking the question is most likely a logical consequence of the prior statement:
Mia demando estas do ĉu ĝi validas aŭ ne
Therefore my question is…
Mia demando estas tial ĉu ĝi validas aŭ ne
That's why my question is…
This boils down to the same thing. In a lot of cases do and tial can be used more or less interchangeably, because if there is a reason that something happens, it is often a logical consequence as well; conversely, if something is a logical consequence, then that fact is a good reason for why it happens.
At the moment I cannot think of a good example to contrast the two meanings better, or where using one word would really give an essentially different sentence than when you would use the other. I'll update my answer if I think of anything.
Tiel means ‘in that manner’. Do means something more like ‘therefore’. Either can be translated ‘thus’, but the senses are not the same.
(Oh dear, maybe I have just now understood why some people insist on thusly: to avoid the do-sense.)
