Hereby the complete reference of the two books I suggest.
The first one is a gentle introduction to logic, and the second
one is in between Jeffrey's one and Boolos 1993.

JEFFREY Richard, "Formal Logics Its Scope and Limits" McGraw-Hill Book
             Company, 1967 (1981 second edition).

BOOLOS G. and JEFFREY R., "Computability and Logic" Cambridge University 
             1974, (1989 third edition).

To be honest this gives one half of the logic needed for the AUDA.
The other half is QUANTUM LOGIC and its modal translation by Goldblatt.
An intro to quantum logic is given at


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