Computational problems & resources come understood in their virtually all general - interactive feel. It is formalized when games played by a machine against its environment, & computability means being of the machine that wins the game against any conceivable behavior per environment. Defining what such game-swimming machines mean, computability logic will bring the generalization of the Church-Turing thesis to the interactive level.

the definitive construct of truth turns bent on exist as a favorite, zero-interactivity-degree experience of computability. This makes authoritative logic the favorite fragment of computability logic. Existence the conservative extension of a former, computability logic is, at the equivalent period, by an sequentially of magnitude additional expressive, constructive & computationally meaningful. Providing the orderly guide to the fundamental wonder "what (and how) can be computed?", it has the wide range of expected application areas. Victims include constructive applied theories, knowledge base systems, systems for planning & action.

Besides authoritative logic, linear logic (understood in the relaxed feel) & intuitionistic logic also turn out to exist as natural fragments of computability logic. Hence meaningful conception of "intuitionistic truth" & "linear-logic truth" may be from either a semantics of computability logic.

Existence semantically constructed, yet computability logic doesn't have a fully developed proof theory. Choosing deductive systems for various fragments of it & researching their syntactical properties is an vicinity of on-going search.

Reference

G. Japaridze, Introduction to computability logic. Annals of Pure & Applied Logic 123 (2003), web sites One-99.