European Research Network on Formal Proofs
COST action CA20111
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In the International School on Logical Frameworks and Proof Systems Interoperability.

Lecturer: Florian Rabe

In this course, I will show how the design and formalization of logics can apply the same modularity principles as commonplace in software design. Using LF-like logical frameworks together with the MMT module system, we can define the syntax and proof theory as well as the semantics of translations between logics elegantly.

As concrete examples, the course will give a tour of the LATIN logic atlas, which holds hundreds of modular building blocks for formal systems, organized multi-dimensionally by (among others)

  • ontology: typed, soft-typed, untyped, …
  • type system features: functions, products, refinements, …
  • logical features: propositional, modal, first-order, higher-order, …

Outline (tentative):

  1. Introduction to LF and MMT, fundamental ontology and basic examples

  2. The Zoo of Type-Theoretical and Logical Features

  3. Homomorphisms for formalizing logic translations, semantics, and soundness proofs

  4. Formalization limits of current frameworks: advanced type-theoretical features, completeness proofs, non-compositional translations