theory and a logic

Question

The book I am reading (The first course in logic) discusses the difference between a logic and logic. This distinction is quite clear to me. I wonder what is the difference between a theory and a logic?

Answer 1

I like to think as logic as the set of rules to a game. If I have $A$ and $A\rightarrow B$, then I can conclude $B$. A theory is a set of starting positions for that game. So, each chess piece has certain ways it can move (logic), but we may initially set up the board in any number of configurations (theory).

More formally, a logic is a list of transformations that you may apply to your assumptions to produce outcomes. A theory usually takes the form of a set of axioms. For instance, a number theory will be a set of axioms that lay out the natural numbers and the various operations we are interested in, like addition and such.