Resource modalities in game semantics

TL;DR

This paper proposes a new categorical model of resources in game semantics, extending the arena game model with multi-bracketing to capture different resource policies like linear, affine, and exponential.

Contribution

It challenges the view that linear logic is more primitive than game semantics and develops a model where game semantics is foundational for resource description.

Findings

Developed a categorical model of resources in game semantics

Extended arena game model with multi-bracketing for resource policies

Unified treatment of linear, affine, and exponential resources

Abstract

The description of resources in game semantics has never achieved the simplicity and precision of linear logic, because of a misleading conception: the belief that linear logic is more primitive than game semantics. We advocate instead the contrary: that game semantics is conceptually more primitive than linear logic. Starting from this revised point of view, we design a categorical model of resources in game semantics, and construct an arena game model where the usual notion of bracketing is extended to multi- bracketing in order to capture various resource policies: linear, affine and exponential.