Propositional computability logic II

Abstract

Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is understood as its being a scheme of problems that always have algorithmic solutions. The earlier article “Propositional computability logic I” proved soundness and completeness for the (in a sense) minimal nontrivial fragment CL1 of computability logic. The present article extends that result to the significantly more expressive propositional system CL2 . What makes CL2 more expressive than CL1 is the presence of two sorts of atoms in its language: elementary atoms , representing elementary computational problems (i.e. predicates), and general atoms , representing arbitrary computational problems. CL2 conservatively extends CL1 , with the latter being nothing but the general-atom-free fragment of the former.