The formal strong completeness of partial monoidal Boolean BI

This article presents a self-contained proof of the strong completeness of the labelled tableaux method for partial monoidal Boolean BI: if a formula has no tableau proof then there exists a counter-model for it which is simple. Simple counter-models are those which are generated from the specific constraints that occur during the tableaux proof-search process. As a companion to this article, we provide a complete formalization of this result in Coq and discuss some of its implementation details. The Coq code is distributed under a free software license and is accessible at http://www.loria.fr/~larchey/BBI.