Arithmetics based on computability logic

Towards applied theories based on computability logic

Computability logic (CL) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, “truth” means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations fo...

Computability and Logic

Intuitionistic computability logic I

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 b...

On abstract resource semantics and computability logic

We show that the uniform validity is equivalent to the non-uniform validity for Blass’ semantics of [A game semantics for linear logic. Annals of Pure and Applied Logic 56 (1992) 183–220]. We present a shorter proof (than that of [G. Japaridze. The intuitionistic fragment of computability logic at the propositional level. Annals of Pure and Applied Logic 147 (2007), No.3, pp.187-227]) of the co...

Intuitionistic computability logic

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 b...