Title: Logics with Bundled Modalities Are Molecular Logics

Speaker: Guillaume Aucher (University of Rennes)

Time: July 10th (Friday), 16:00 - 18:00

Location: Room 106, Lee Shau Kee Humanities Buildings No.2 (李兆基人文学苑2号楼106)

Abstract:

Atomic logics are based on Dunn's Gaggle theory and generalise modal logics and the Lambek calculus. Sound and complete Hilbert, display and sequent calculi for basic first-order atomic logics with a Kripke-semantics are introduced. These calculi can be automatically computed from the very definition of the connectives of any basic first-order atomic logic. Molecular logics are logics whose molecular connectives are combinations of atomic connectives. We show that bundled modalities are molecular connectives. The correspondence theory for the framework of atomic and molecular logics is then developed on the basis of the work of Goranko & Vakarelov. We obtain correspondence theorems for atomic and molecular logics, with and without information order. We apply our general results to some case studies, FDE, relevance logics, intuitionistic logic and intermediate logics, and we obtain novel axiomatizations.