A Substructural Epistemic Resource Logic: Theory and Modelling Applications

TL;DR

This paper introduces a novel substructural epistemic logic based on Boolean BI, integrating resource-sensitive semantics with epistemic modalities to model agents' local resources and their influence on knowledge.

Contribution

It develops a new logic combining Boolean BI's resource semantics with epistemic modalities, providing formal tools for modeling resource-aware epistemic systems.

Findings

Introduces a new substructural epistemic logic based on Boolean BI.

Provides a labelled tableaux calculus with soundness and completeness.

Demonstrates applications in access control and resource management.

Abstract

We present a substructural epistemic logic, based on Boolean BI, in which the epistemic modalities are parametrized on agents' local resources. The new modalities can be seen as generalizations of the usual epistemic modalities. The logic combines Boolean BI's resource semantics --- we introduce BI and its resource semantics at some length --- with epistemic agency. We illustrate the use of the logic in systems modelling by discussing some examples about access control, including semaphores, using resource tokens. We also give a labelled tableaux calculus and establish soundness and completeness with respect to the resource semantics.