On abstract resource semantics and computability logic
The paper consists of two sections, focused on Japaridze's abstract resource semantics and computability logic, respectively. The first section introduces a formal definition of a semantics for the ``logic of resources'' based on the notion of \textit{accomplishable formula}; this semantics coincides with \textit{G. Japaridze}'s semantics defined in [Ann. Pure Appl. Logic 117, No.~1--3, 261--293 (2002; Zbl 1013.03017)] and later extended to the abstract resource semantics. The relation between accomplishable formulae and, firstly, affine logic and, secondly, with intuitionistic propositional logic is presented. The second part of the paper focuses on computability logic, whose semantics is given in terms of the notions of static games and \textit{winnable formula}. The main result of this section is that the notions of accomplishability and winnability coincide. Moreover, a partial answer to a conjecture in [\textit{G. Japaridze}, Ann. Pure Appl. Logic 123, No.~1--3, 1--99 (2003; Zbl 1028.03025)] is given, by proving that uniform winnability coincides with non-uniform winnability; however, the initial conjecture ``computable winnability coincides with uniform computable winnability'' remains open.
positive fragment of intuitionistic logic
scientific article; zbMATH DE number 5731996
scientific article