Third Nordic Logic Summer School, Stockholm 2017

Categorical Logic

Course description

Categorical logic studies the interpretation of logical theories in categories and the interplay between formal theories and categories. As such, it is abstract algebraic logic extended to predicate logic and beyond. Categorical semantics provides a wide variety of models for various formal languages and theories, including for intuitionistic first- and higher-order logic. Moreover, the categorical framework provides a rich conceptual background for constructions and perspectives that are not (always so easily) obtainable in the more classical model theoretic setting.

This course gives a first introduction to central ideas and concepts in categorical logic. We shall focus primarily on first-order logic, including intuitionistic first-order logic and fragments of first-order logic. Prerequisites will be kept to a minimum, with an initial emphasis on from-the-ground-up explanations of the categorical interpretation of the logical constants, examples of interpretations is various categories, the familiar Tarski and Kripke semantics as special cases, the models-as-functors perspective, and the construction of universal models. On this basis, we will give pointers to and discuss further topics, such as higher-order logic, forcing semantics, duality between syntax and semantics, and type theories (depending on time and interest).

Course material

Course schedule

In parenthesis the sections of the prelecture notes that that part is based on, in the sense that one should really at least have had a good look at it before the lecture.

  1. day
  2. day
  3. day
  4. day
  5. day