A new book of logic
K Nour, C Raffalli and myself have written a book of logic with
particular emphasis on proof theory:
This book, written in French, is mostly destinated to undergraduate
students but can be used also by graduate ones.
The summary is :
- First order logic. Natural deduction. Examples in ordinary
- Semantics of first order logic. Completeness theorem. Compactness
theorem. A bit of model theory.
- Algebraic theories. Peano arithmetic. Set theory. Incompletness
results. Quantifier elimination. Examples of decidable theories.
- Minimal and intuitionistic logic. Gödel and Kuroda translation. Kripke
models. Heyting arithmetic.
- Sequent calculus. The theorem on the elimination of cuts and its
- Higher order logics.
- Automated deduction. Unification, resolution and the tableaux method.
- The proof assistant PhoX.
- Solutions of the exercices.