Many-sorted Logic and Its Applications (Jouko Väänänen)

[updated on 2014.07.08]

Instructor: Jouko Väänänen (University of Helsinki and the University of Amsterdam)

Title: Many-sorted logic and its applications

Abstract: In many-sorted logic we have several “sorts” of variables, just as in vector spaces we have scalars and vectors, or as in geometry we have points and lines, or as in second order logic we have individuals and subsets, or as in databases we can have fields with different ranges of values. Although many-sorted logic can be translated into one-sorted logic it is often more natural to take the many-sorted approach, and sometimes the many-sorted version of a fundamental theorem is more powerful than the single sorted version. This is the case, for example, with the Craig Interpolation Theorem which we prove in the many-sorted version. We will discuss various applications of many-sorted logic, among others applications of the many-sorted interpolation theorem. Time permitting, we will learn a little set theory and develop a “symbiosis” between set theory and model theory, based on many-sorted logic.

Lecture slides (updated July 8 11:55)

Exercise Group 1

Exercise Group 2

Exercise Group 3

Useful online book by the course teacher

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