Title：On Lindström Theorems for Some Modal Logics

Speaker：Diego Fernandes (Universidade Federal da Paraíba)

Time: 2024/12/03 15:10-18:00

Location: Room 206, Building of Geometry (地学楼), Peking University

Abstract:

In the seminar I will briefly review the original Lindström theorem (1969) characterizing first-order logic as the most expressive system having compactness and Löwenheim-Skolem. In the sequel some Lindström-type theorems for modal logics will be presented, each following a different proof strategy. The first, due to de Rijke (1995) and van Benthem (2007), characterizing basic modal logic. The second, due to Otto and Piro (2010) characterizing the modal logic with a universal modality and the third, due to Fernandes (2024), characterizing the hybrid logic with existential quantifier. These three ways to obtain Lindström theorems will be compared and discussed in the end.

References:

Fernandes, D. (2024). A Lindstrom Theorem for the Hybrid Logic H(∃). (To appear)

Lindström, P. (1969). On extensions of elementary logic. Theoria, 35 (1), 1–11. doi: 10.1111/j.1755-2567.1969.tb00356.x

Otto, M., & Piro, R. (2010). A lindström characterisation of the guarded fragment and of modal logic with a global modality. In L. Beklemishev, V. Goranko, & V. Shehtman (Eds.), Advances in modal logic, volume 8. College Publications.

Rijke, M. D. (1995). A lindström theorem for modal logic. In Modal logic and process algebra (pp. 217–230). CSLI Publications

van Benthem, J. (2007). A new modal lindström theorem. Logica Universalis, 1 (1), 125–138. doi: 10.1007/s11787-006-0006-3