Bifurcation Logic: Separation Through Ordering

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.