Quantified Modal Logic

Welcome to the homepage for MoL project Quantified Modal Logic: Philosophical, Logical and Pedagogical aspects.

This is a project taught in January 2026 by Pablo Rivas-Robledo and Tom Schoonen.

Notes & Recordings

Below you will find the notes that we used for the project and the recoding of the sessions.

QML_notes.pdf

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.

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.

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.

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