What is a logical move? I'm not sure as to what constitutes as a logical move. Sometimes I hear that chess is a discussion using statements, arguments, questions and answers. 

Can someone explain to me what a logical move would be given this context? A nice, practical example would also be of great help to me.
A move which is obviously not bad to play. It's a fuzzy word to describe and evaluate a move, so it's hard to explain (it's strongly opinion based). Maybe we can put a logical move in the middle of this list:

!!  an excellent move
!   a particularly good—and usually surprising—move
!?  an interesting move that may not be best
&gt;&gt;&gt; Logical move is here and contains above &lt;&lt;&lt;
?!  a dubious move – one which may turn out to be bad
?   a bad move
??  a blunder


Although, ideally speaking, the logical move is the best move, but It may not the case in your question.

Consider this position between Anand.V vs. Carlsen.M - the World Championship match. For an average rated player there're many logical moves such as 1.R4c3, 1.Rd1 and even 1.Kg2. By playing those moves his coach will not criticize him and he will say OK you made a logical move. But..

r3b3/1kp5/1pn1P1p1/pN6/2R3Pr/1P6/5N2/2R3K1 w - - 1 35


In the world championship between two giants, the only logical move is 1.Ne4! which is played also. (Even my chess engine find it hard)

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A hint from Karpov, exact calculation in a game is much preferred rather than general guidelines. Guidelines do not find the best or logical move, they will be used to find logical candidate moves and then a exact move calculation will find the best move from the list. See the example again, a general guideline says try to protect your pieces but a comprehensive calculation says another thing. Ne4!. Which one is logical for GMs ?!