This page introduces my works on using formal systems to understand and model human knowledge systems.
Epistemic Syllogistics
Together with Yanjing Wang, we investigated epistemic syllogistics. We took a modern perspective on the systems of epistemic syllogistics, as a natural logic that models people’s everyday epistemic reasoning. Treating the syllogistics formally as a fragment of first order modal logic, we investigated theoretical properties of the systems and proved completeness. Our work appears as: Epistemic Syllogistic: First Steps joint with Yanjing Wang in Tark 2023. preprint
Propositional quantifiers
Propositional quantifiers are powerful tools to model people’s epistemic and doxastic systems (people’s reasoning involving their or others’ knowledge and belief). That’s because propositional quantifiers allows us to quantify over people’s knowledge and express things like ‘Everything Socrates knows is true.’, which are otherwise inexpressible without quantifying over propositions. Together with Yifeng Ding, we investigated the theoretical properties of propositional quantifiers and gave the first general axiomatization result for propositionally quantified modal logic. Our work appears as: Some General Completeness Results for Propositionally Quantified Modal Logics joint with Yifeng Ding in AiML 2024. preprint