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Mathematical Logic Foundations

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Mathematical Logic Foundations

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Research Frontiers in Constructive Type Theory and Dependent Types

Studies formal systems where propositions are types and proofs are computational terms, focusing on constructive mathematics without classical logic.

Computational Meaning in Dependent Type Theories
Homotopy Type Theory and Higher Dimensional Structures
Constructive Semantics of Infinite Types and Coinduction
Proof Irrelevance and Observational Type Equivalence
Cubical Type Theory and Computational Path Semantics
Linear and Substructural Dependent Type Systems
Decidability Frontiers in Dependent Type Checking
Modal Operators in Constructive Dependent Logics
Univalent Foundations and Category-Theoretic Meaning
Termination and Productivity in Dependent Recursion

All Mathematical Logic & Foundations PhD categories