Bifurcation Logic: Separation Through Ordering

TL;DR

Bifurcation Logic (BL) introduces a novel combination of classical modality with separating conjunction and a related implication, providing a new logical framework with decidability results and applications in multi-agent access control.

Contribution

This paper presents Bifurcation Logic, a new logic combining modal and separating conjunction, with a labelled tableaux calculus, completeness, and decidability results, and demonstrates its application in multi-agent systems.

Findings

BL has a labelled tableaux calculus ensuring soundness and completeness.

Finite model property fails for BL with implication, but models are finite without it.

BL can model multi-agent access control scenarios effectively.

Abstract

We introduce Bifurcation Logic, BL, which combines a basic classical modality with separating conjunction * together with its naturally associated multiplicative implication, that is defined using the modal ordering. Specifically, a formula A*B is true at a world w if and only if each of A,B holds at worlds that are each above w, on separate branches of the order, and have no common upper bound. We provide a labelled tableaux calculus for BL and establish soundness and completeness relative to its relational semantics. The standard finite model property fails for BL. However, we show that, in the absence of multiplicative implication, but in the presence of *, every model has an equivalent finite representation and that this is sufficient to obtain decidability. We illustrate the use of BL through an example of modelling multi-agent access control that is quite generic in its form, suggesting many applications.