Abstract
Qualitative logical modelling techniques play an important role in biology and are seen as crucial for developing scalable methods for modelling and synthesizing biological systems. While a range of interesting work has been done in this area there still exists challenging issues that need to be addressed for the practical application of these modelling techniques. In this paper we present an algebraic framework for exploring these issues by developing techniques for modelling and analysing qualitative biological models using Rewriting Logic (RL). The aim here is to develop a universal formal framework which is able to integrate models expressed in different formalisms (e.g. Boolean networks, Petri Nets and process algebra) and provide a basis for new work in this area (e.g. merging models based on different formalisms; compositional model construction and analysis; and tools for synthetic biology). We take as our starting point Multi-valued networks (MVNs), a simple yet expressive qualitative state based modelling approach widely used in biology. We develop a semantic translation from MVNs to a corresponding RL model and formally show that this translation is correct. We consider both the asynchronous and synchronous update semantics, and investigate the use of rewriting strategies to enable synchronisation to be modelled. We illustrate the RL framework developed and the potential RL analysis possible by presenting two detailed case studies.