A Note on an Inferentialist Approach to Resource Semantics

TL;DR

This paper explores how inferentialism provides a flexible framework for resource semantics, integrating logic of Bunched Implications and Linear Logic to improve reasoning about system resources.

Contribution

It demonstrates how inferentialism enhances resource semantics by unifying assertion-based and usage-based interpretations within a versatile framework.

Findings

Integrates assertion-based and usage-based resource semantics.

Enables intuitive reasoning about shared and separated resources.

Facilitates reasoning about system component composition.

Abstract

A central concept within informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their behaviour and properties. To this end, one requires an interpretation of logical formulae in terms of the resources and states of the system; such an interpretation is called a 'resource semantics' of the logic. This paper shows how 'inferentialism' -- the view that meaning is given in terms of inferential behaviour -- enables a versatile and expressive framework for resource semantics. Specifically, how inferentialism seamlessly incorporates the assertion-based approach of the logic of Bunched Implications, foundational in program verification (e.g., as the basis of Separation Logic), and the renowned number-of-uses reading of Linear Logic. This integration enables reasoning about shared and separated resources in intuitive and familiar ways, as well as about the composition and interfacing of system components.