1st Semester 2025/26: Quantified Modal Logic: Philosophical, Logical and Pedagogical aspects

Instructors

Pablo Rivas-Robledo and Tom Schoonen

ECTS

6

Description

• Quantified Modal Logic (QML) is a family of logics that deals with quantified statements which contain modal operators. Importantly, this allows for the expression of statements that involve not just what is possible or necessary, but also how modalities can vary across different individuals in different possible worlds.
• Despite its intuitive appeal, coming up with systems that satisfy our philosophical and mathematical requirements its a difficult task. This project is an introduction to the many approaches to QML from a semantical point of view. The aim of the project is for the students to study and familiarise themselves with the many semantics for QML.
• Special track: There would a special track for students interested in re-writing Chapter 3 of Gamut's "Logic, Language and Meaning, vol. 2" based on the topics studied in the project. This special track will be lead by the instructor.

Organisation

• TL:DR: Lectures during the first two weeks, student presentations during the fourth week.
• This project will be taught in a hybrid format.
• Here's a tentative schedule:
• Week 1: Philosophy first, mathematics second
• Lecture 1: Basic propositional and quantified modal logic
• Lecture 2: QML with identity via relational semantics
• Lecture 3: QML with identity via a second-order logic
• Lecture 4: QML via free logic and proof-theoretic semantics
• Week 2: Mathematics first, philosophy second
• Lecture 5: QML with identity via Kripke frames and Kripke sheaves
• Lecture 6: QML with identity via admissible models
• Lecture 7: QML with identity via predicate abstraction
• Two guest lectures (exact date to be confirmed):
• Impossible world semantics (Tom Schoonen, ILLC-UvA)
• Identity in type theory (Fernando Chu, Utrecht)

Prerequisites

• Familiarity with first-order logic and Kripke semantics for modal logic.
• Familiarity with the with metaphysical/philosophical debates in QML is not necessary but welcome.

Assessment

• On week four all students should give one presentation of roughly 1:30h. Presentations should consist of a more in-depth presentation of one of the semantics studied or an introduction to other semantical approaches (non-deterministic, relational model structures, etc.*).
• At the end of week four students should submit a short written summary of their research.