Interpreting Sequent Calculi as Client-Server Games

摘要

Motivated by the interpretation of substructural logics as resource-conscious reasoning, we introduce a client-server game characterizing provability in single-conclusion sequent calculi. The set up is modular and allows to capture multiple logics, including intuitionistic and (affine) linear intuitionistic logic. We also provide a straightforward interpretation of subexponentials, and moreover introduce a game where the information provided by the server is organized as a stack, rather than as a multiset or list.