Yes, LOGICS is a Scrabble word!

Letter values in Scrabble US: L 1, O 1, G 2, I 1, C 3, S 1.

Is it a valid word?

LOGICS is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

the branch of philosophy that analyzes inference
reasoned and reasonable judgment
the principles that guide reasoning within a given field or situation
the system of operations performed by a computer that underlies the machine's representation of logical operations
a system of reasoning

Also: logical system, system of logic.