Projects & Grants

Internal Grant Competition DGC

Metamathematics of substructural modal logics
Project Id22-01137S
Main solverMgr. Libor Běhounek, Ph.D.
Period1/2022 - 12/2024
ProviderStandardní projekt GA ČR
AnotationClassical logic models reasoning about Boolean combinations of atomic propositions. Modal logics extend it by adding propositional connectives (called `modalities') to allow reasoning about the modes of truth, such as `necessarily', `is allowed', or `is known'. Conversely, substructural logics relax assumptions on logical atoms to allow reasoning about other interesting objects such as constructive proofs, resources, or the degrees of truth. There are deep mathematical theories available for both classes of logics, which both aid their applications in mathematics, computer science, economics, linguistics, etc., and are of independent mathematical interest. This is, however, not the case for their combination, which hinders their development and application potential. The goal of the project is to advance three underdeveloped areas of substructural modal logics by creating general theories of algebravalued frames and logics with layered syntax and establishing the foundations of quantified substructural modal logics.