The intuitionistic fragment of computability logic at the propositional level

This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games between a machine and its environment. Intuitionistic implication is understood as algorithmic reduction in the weakest possible — and hence most natural — sense, disjunction and conjunction as deterministic-choice combinations of problems (disjunction = machine’s choice, conjunction = environment’s choice), and “absurd” as a computational problem of universal strength.