Section: New Results

Encoding Bigraph Structure with Subexponentials

Participants : Kaustuv Chaudhuri, Giselle Reis.

Bigraphs were proposed by Robin Milner as a model of ubiquitous computing, which is computation that is aware both of location and of connections. As a formalism it subsumes many other process calculi such as CCS and the $\pi$-calculus. However, it has a number of problems qua syntax because it is based on graphs and a complicated theory of composition. The biggest of these problems is how to implement it in a formal reasoning system.

In recent years, many members (and ex-members) of the Parsifal team have been experimenting with a variant of linear logic that has not just a single pair but an arbitrary family of exponential connectives that are arranged in a pre-order. Each such pair of subexponentials may admit or reject the structural properties of weakening and contraction. One benefit of subexponentials is that it allows for querying the absence of certain kinds of exponential formulas without requiring all non-exponential formulas to be deleted as a consequence, which is the issue with ordinary linear logic.

In [28] (LPAR'15), we show how to represent the structure of bigraphs in terms of a simple theory of linear logic with subexponentials (SEL). We show that our representation is adequate, i.e., that it respects the composition and juxtaposition operations on bigraphs. Moreover, we show how one can ask queries about the nesting of places in the representation without modifying it, which gives us a technical means of encoding bigraph reactions as well. Some of the details for bigraph reactions remain to be worked out in future work.