  Computability logic (see http://www.csc.villanova.edu/~japaridz/CL/) is a
long-term project for redeveloping logic on the basis of a constructive game
semantics, with games seen as abstract models of interactive computational
problems. Among the fragments of this logic successfully axiomatized so far is
CL12 --- a conservative extension of classical first-order logic, whose
language augments that of classical logic with the so called choice sorts of
quantifiers and connectives. This system has already found fruitful
applications as a logical basis for constructive and complexity-oriented
versions of Peano arithmetic, such as arithmetics for polynomial time
computability, polynomial space computability, and beyond. The present paper
introduces a third, indispensable complexity measure for interactive
computations termed amplitude complexity, and establishes the adequacy of CL12
with respect to A-amplitude, S-space and T-time computability under certain
minimal conditions on the triples (A,S,T) of function classes. This result very
substantially broadens the potential application areas of CL12. The paper is
self-contained, and targets readers with no prior familiarity with the subject.
