Our global aim is to elaborate a number of frameworks with which to quantify properties of boolean structures (circuits, proof systems, formulae, and functions). In other words, we want to be able to model, measure, and predict probabilistic properties, typically, average values, variances, moments, limiting distributions of well-defined models. Our project is indeed focused on important average-case and probabilistic aspects. In this perspective, we propose to extract and formalise four central boolean frameworks:

• Circuits and Boolean Normal Forms (BNF);
• Boolean functions and cryptography;
• Satisfiability (SAT);
• Quantitative logic.

We shall organise problems into a few broad categories susceptible to analysis. To this purpose we shall endeavour to develop two major methodological axes:

• Combinatorial and analytic methods;
• Probabilistic methods.

Our project is targeted at fundamental research in these six areas.