Abstract model theory for non-classical logics: seeing the bigger picture behind the growing diversity

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Non-classical logics are proliferating, both in computer science and in current philosophy. This is great, but then the foundational perspective, allowing to see the bigger picture behind this manifold growth, becomes especially valuable. This project proposes one such big picture attempt. The project is primarily concerned with achieving new abstract semantical characterizations for a rather wide class of logical systems situated below classical first-order logic (FOL) in terms of their expressive power. The proposed inquiry is going to proceed on a high level of abstraction, which brings it to the realm of abstract or 'soft' model theory for the said logics. We are mainly going to look into the results inspired by the Modal Characterizaton Theorem by J. van Benthem on the one hand, and by P. Lindström characterization of FOL on the other hand, allowing to chart big chunks of the landscape of non-classical logics and to gain insight into their composition.To assess the success of this approach, two groups of benchmark examples will be used, namely, substructural logics and the logics related to intuitionistic propositional logic.