Computability logic: Giving Caesar what belongs to Caesar

Abstract

The present article is a brief informal survey of computability logic --- the game-semantically conceived formal theory of computational resources and tasks. This relatively young nonclassical logic is a conservative extension of classical first order logic but is much more expressive than the latter, yielding a wide range of new potential application areas. In a reasonable (even if not strict) sense the same holds for intuitionistic and linear logics, which allows us to say that CoL reconciles and unifies the three traditions of logical thought (and beyond) on the basis of its natural and "universal" game semantics. A comprehensive online survey of the subject can be found at http://www.csc.villanova.edu/~japaridz/CL/ .