Logicaly or Logically, this is the question.

[Aiwen]

Both spellings may be found.
Who is the authority that decides in these questions?

 

[bhaisahab]

Both spellings may be found.
Who is the authority that decides in these questions?

"Logicaly" is incorrect.

 

[Nightmare85]

***Neither a teacher nor a native speaker.***

Both spellings may be found.

A lot of things may be found, but you should not pay attention to everything you read.

The general rule is to add an -ly on an adjective when you want to make an adverb out of it.
Of course there are exceptions, but when it ends on an l, you can simply add an -ly.
Normal -> Normally
Usual -> Usually
Grammatical -> Grammatically
Logical -> Logically

As said, don't take the rule too seriously, but these 4 examples should show you how to handle such words.

Cheers!

 

[Aiwen]

Thank you Shaisahab for your answer.
Dankeschoen Nightmare because besides giving me a fish you also taught me to fish.

Cheers!