Modal logics are a family of formal systems based on classical logic which aim at improving the expressive power of the

classical calculus allowing to reason about “modes of truth”. The aim of the present proposal is to put forward a systematic

study of substructural modal logics, understood as those modal logics in which the modal operators are based upon the

general ground of substructural logics, weaker deductive systems than classical logic. Our aim is also to explore the

applications of substructural modal logics outside the bounds of mathematical logic and, in particular, in the areas of

knowledge representation; legal reasoning; data privacy and security; logical analysis of natural language.