Section: Scientific Foundations
A logic for systems biology
Systems in molecular biology, such as those for regulatory gene networks or protein-protein interactions, can be seen as state transition systems that have an additional notion of rate of change. Methods for specifying such systems is an active research area. However, to our knowledge, no logic (more powerful than the boolean logic) have been proposed so far to both specify and reason about these systems.
One current and prominent method uses process calculi, such as the stochastic -calculus, that has a built in notion of rate  . Process calculi, however, have the deficiency that reasoning about the specifications is external to the specifications themselves, usually depending on simulations and trace analysis.
Kaustuv Chaudhuri and Joëlle Despeyroux are considering the problem of giving a logical instead of a process-based treatment both to specify and to reason about biological systems in a uniform linguistic framework. The logic they have proposed, called HyLL, is an extension of (intuitionistic) linear logic with a modal situated truth that may be reified by means of the operator from hybrid logic . A variety of semantic interpretation can be given to this logic, including the rates and the delay of formation.
The expressiveness of the logic has been demonstrated on small examples and first meta-theoretical properties of the logic have been proven. Considerable work needs to be done before this proposal succeeds as a natural logical framework for systems biology. Remaining work mainly includes the description of larger examples (requiring more specifications of usual biological notions), and automating reasoning about the specifications. It also includes further studies of the meta-theoretical properties of the logic, and of course eventual extensions of the logic (for example to get branching semantics).