3月29日，Wesley Holliday教授作了题为《Modal logic, fundamentally》的报告。

　　First, Prof. Holliday introduced fundamental logic. In a Fitch-style natural deduction system, the fundamental logic contains only the introduction and elimination rules for the logical constants. If one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; if instead of adding Reiteration, one adds the rule of Reductio ad Absurdum, one obtains a proof system for orthologic; by adding both Reiteration and Reductio, one obtains a proof system for classical logic. Prof. Holliday also gave algebraic semantics and relational semantics for this logic.

　　Next, Prof. Holliday Extended fundamental logic with modality. He gave the definition of modal frame and some frame properties, then a general approach via algebraic representation theorems were discussed. Finally, Prof. Holliday proposed the fundamental modal logic and showed a completeness result for this logic.

——王云崧