Objectives

Introduction to formal logics.

Contents

Logic is often presented as the art of reasoning well. It is the discipline of deduction, rigorous proofs, mechanical evidence. But it is also the location of interpretations of the meaning of statements, and that of models or possible worlds. This course takes place in the heart of the difference between syntax and semantics. Every time we will analyze how the framework operates-

After recalling a few basics on set theoretic operations, we will apply them to the resolutions of the syllogisms of Aristotlle. We will investigate how a proof works. Then we will study various fundamental logics:

1) Propositional logic: a logic with a weak expressie power but bearing the advantage of presenting the basic concepts essential to the development of other more involved logics.

2) The modal logic dealing with modalities such as to know / to believe, obligation / permission; necessity / possiblility in the semantics of possible worlds.

3) predicate logic: a much more advanced logic, with a high expressive power, but still easy to appprehend.

References

[1] Jacques Duparc. La logique pas à pas. PPUR, 2015

[2] Robert Blanché. Introduction à la logique contemporaine. Armand Colin, 1997.

[3] André Delessert. Introduction à la logique. Presses polytechniques romandes, 1988.

[4] A. Olza G. Haury, R. Lang. Eléments de logique. Lausanne : Spes ; Paris : Dunod, 1973. 135 p.; 21 cm.

[5] J.L. Krivine G. Kreisel. Eléments de logique mathématique : théorie des modèles. Paris : Dunod, 1967. VIII, 212 p. : ill. ; 25 cm.

[6] M.J. Cresswell G.E. Hughes. A new introduction to modal logic. London ; New York : Routledg, 2003. X, 421 p.; 23 cm.

[7] D. Lascar R. Cori. Logique Mathématique. Cours et exercices. vol 1. Calcul propositionnel, algèbres de Boole, calcul des prédicats. Paris : Masson, 1993.

[8] D. Lascar R. Cori. Logique Mathématique. Cours et exercices. vol 2. Fonctions récursives, théorèmes de G ̈odel, théorie des ensembles, théorie des modèles. Paris : Masson, 1993.

[9] Christophe Raffalli René David, Karim Nour. Introduction à la logique : théorie de la démonstration : cours et exercices corrigés. Paris : Dunod, 2001. XII, 332 p. : ill. ; 24 cm.

Pre-requisites

None

Evaluation

First attempt

Exam:

Written 2 hours

Documentation:

Allowed with restrictions

Calculator:

Not allowed

Evaluation:

Final exam (an A4 two side sheet of personal notes is allowed).

Retake

Exam:

Written 2 hours

Documentation:

Allowed with restrictions

Calculator:

Not allowed

Evaluation:

Final exam (an A4 two side sheet of personal notes is allowed).