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Section: New Results

Temporal Logic Constraint Solving in QFLTL(R)

Participants : François Fages, Aurélien Rizk.

Temporal logics and model-checking are at the core of BIOCHAM to express biological properties of complex biochemical systems and automatically verify their satisfaction in both qualitative and quantitative models. In [3] , we go beyond model-checking and present a constraint solving algorithm for quantifier-free first-order temporal logic formulae with constraints over the reals, denoted by QFLTL(R). This algorithm computes the domain of the real valued variables occurring in a formula that makes it true in a model. We illustrate this approach for the automatic generation of a temporal logic specification from biological data time series. We provide a set of biologically relevant patterns of formulae, and apply them to numerical data time series of models of the cell cycle control and MAPK signal transduction. We show in these examples that this approach infers automatically semi-qualititave semi-quantitative information about concentration thresholds, amplitude of oscillations, stability properties, checkpoints and influences between species.


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