Toggling operators in computability logic

Toggling operators in computability logic

Computability logic (CL) is a recently introduced semantical platform and research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been. Formulas in CL stand for interactive computational problems, seen as games between a machine and its environment; logical operators represent operations on such entiti...

Sequential operators in computability logic

Computability logic (CL) is a semantical platform and research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been. Formulas in CL stand for (interactive) computational problems, understood as games between a machine and its environment; logical operators represent operations on such entities; and “tru...

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...

Open problems in computability logic

1. Remark 7 of [6] claims that the cirquent calculus system CL5 without duplication has polynomial size proofs (every provable formula F has a proof whose size is polynomial in the size of F ). Verify this claim. What kind of a polynomial do we have here? Does such a system have any reasonable semantics? 2. Consider the system CCC from [6] but without the Weakening rule. Does it have an interes...