About the project
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 algebra valued frames and logics with layered syntax and establishing the foundations of quantified substructural modal logics.
The is a joint project of the Institute of Computer Science of the Czech Academy of Sciences and the Institute for Research and Applications of Fuzzy Modeling of the University of Ostrava funded by the Czech Science Foundation, grant no. 22-01137S. It runs from January 2022 till December 2024.
Project team
Publications
Papers in journals
- [1] N. Ferenz and A. Tedder: Neighbourhood Semantics for Modal Relevant Logics. Journal of Philosophical Logic, 2022.
Papers in conference proceedings
- [1] P. Cintula, G. Metcalfe and N. Tokuda: Algebraic Semantics for One-Variable Lattice-Valued Logics. To appear in: D. Fernández-Duque, A. Palmigiano (Eds.): Proc. 14th Int. Conference on Advances in Modal Logic (AiML 2022). College Publications, 2022.
- [2] I. Sedlár and P. Vigiani: Relevant Reasoners in a Classical World. To appear in: D. Fernández-Duque, A. Palmigiano (Eds.): Proc. 14th Int. Conference on Advances in Modal Logic (AiML 2022). College Publications, 2022.
Book chapters
- [1] N. Ferenz: Conditional FDE Logics. In: K. Bimbo (Ed.): Essays in Honour of J. Michael Dunn, pp. 182–214. College Publications, 2022.