The course of Logical Theories 1 is part of the program in Philosophical Sciences (MA level) and is included among the complementary training activities. The objective of the course is to provide an in-depth understanding of some aspects of the essential issues and debates connected to the field Logical Theories 1. The golas of the course is to acquire a basic knowledge of Zermelo-Fraenkel axiomatic set theory.
teacher profile teaching materials
A) STRUCTURAL RULES INTERPRETED AS LOGICAL RULES: SEQUENT CALCULUS AND DERIVABILITY IN LINEAR LOGIC
B) POSITIVE AND NEGATIVE NON-DETERMINISM: FOCUSED SEQUENT CALCULUS FOR LINEAR LOGIC AND PROOF SEARCH
C) IMPLICIT COMPLEXITY AND LINEAR LOGIC
D) GEOMETRY OF PROOFS: PROOF NETS IN LINEAR LOGIC
E) INVARIANTS AND DEVELOPMENT OF INTERACTION OF PROOFS: COHERENT SPACES, GEOMETRY OF INTERACTION
Programme
A) STRUCTURAL RULES INTERPRETED AS LOGICAL RULES: SEQUENT CALCULUS AND DERIVABILITY IN LINEAR LOGIC
B) POSITIVE AND NEGATIVE NON-DETERMINISM: FOCUSED SEQUENT CALCULUS FOR LINEAR LOGIC AND PROOF SEARCH
C) IMPLICIT COMPLEXITY AND LINEAR LOGIC
D) GEOMETRY OF PROOFS: PROOF NETS IN LINEAR LOGIC
E) INVARIANTS AND DEVELOPMENT OF INTERACTION OF PROOFS: COHERENT SPACES, GEOMETRY OF INTERACTION
Core Documentation
NOTES AND SLIDES AVAILABLE ON THE COURSE WEB PAGEReference Bibliography
Main reference articles on linear logic available on the Jean-Yves Girard web page https://girard.perso.math.cnrs.fr/Archives.htmlType of delivery of the course
LESSONS WITH EXERCISESAttendance
attendance is not mandatory but strongly encouragedType of evaluation
questions and exercises on the topics covered in class