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. Blass, A game semantics for linear logic, Ann. Pure Appl. 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, Ann. Pure Appl. Logic 147 (3) (2007) 187–227]) of the completeness of the positive fragment of intuitionistic logic for this semantics, computability logic semantics, and the abstract resource semantics.