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
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
https://sites.google.com/view/lm510/
Programme
A) STRUCTURAL RULES INTERPRETED AS LOGICAL RULES: SEQUENT CALCULUS AND DERIVABILITY IN LINEAR LOGICB) 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 PAGEhttps://sites.google.com/view/lm510/
Reference Bibliography
J.-Y. Girard, Proofs and Types AA.VV., Handbook of Linear Logic V. Danos and L. Regnier, The structure of Multiplicatives O. Laurent, Sequentialization of Multiplicative Proof Nets J.-M. Andreoli and R. Maieli, Focusing and proof nets in linear and non-commutative logic R. Maieli, Cut Elimination for Monomial Proof Nets of the Purely Multiplicativeand Additive Fragment of Linear Logic D. Mazza, Attack of the Exponentials C. Retoré, On the relation between coherence semantics and multiplicative proof netsType of delivery of the course
LECTURES WITH EXERCISESType of evaluation
questions and exercises on the topics covered in class