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Characterizing state repertoire and dynamics of spontaneous brain activity by neuroimaging methods

GA21-32608S [Registered results] 2021 - 2024

Current psychological theory provides complex description of mental functions and processes. It is generally accepted that mental functions have brain as their substrate, and that mental processes and states are reflected in brain activity dynamics. A rapidly developing area of brain research is the study of spontaneous brain activity with functional magnetic resonance imaging, allowing simultaneous measurement of activity dynamics of a plethora of brain networks. It has been suggested that during resting state condition, the brain explores its dynamic repertoire of possible states. However, the structure and dynamics of such exploration remains elusive. We propose to use a combination of data analysis techniques, simultaneous EEG/fMRI measurement of both spontaneous and richly stimulated mental activity and comparison with the ever-growing body of functional neuroanatomical knowledge to characterize the state repertoire and transition dynamics of spontaneous mental activity as observable by neuroimaging methods.

Metamathematics of substructural modal logics

GA21-32608S [Registered results] 2022 - 2024

Classical 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.