Computability logic (CL) is a systematic formal theory of computational tasks
and resources, which, in a sense, can be seen as a semantics-based alternative
to (the syntactically introduced) linear logic. With its expressive and
flexible language, where formulas represent computational problems and "truth"
is understood as algorithmic solvability, CL potentially offers a comprehensive
logical basis for constructive applied theories and computing systems
inherently requiring constructive and computationally meaningful underlying
logics.
Among the best known constructivistic logics is Heyting's intuitionistic
calculus INT, whose language can be seen as a special fragment of that of CL.
The constructivistic philosophy of INT, however, has never really found an
intuitively convincing and mathematically strict semantical justification. CL
has good claims to provide such a justification and hence a materialization of
Kolmogorov's known thesis "INT = logic of problems". The present paper contains
a soundness proof for INT with respect to the CL semantics. A comprehensive
online source on CL is available at http://www.cis.upenn.edu/~giorgi/cl.htm
