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Introduction à la logique

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

 Jacques Duparc. La logique pas à pas. PPUR, 2015

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

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

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

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

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

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

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

 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.

 Franois Rivenc. Introduction à la logique. Payot, 2003.

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Evaluation

First attempt

Exam:
Written 2 hours
Documentation:
Allowed with restrictions
Calculator:
Not allowed
Evaluation:

The evaluation procedures are detailed below. Obtaining grades M1 and M2 is optional, however, these grades do not lower the final grade N. Therefore we may only encourage students to participate in the process of continuous assessment. Students, individually solve the exercises that are proposed on line each week. The six-month average of these scores is M1 (0--100, not rounded). In the middle of the semester, students take a written test resulting in a grade M2 (0--100). At the end of the semester, students take a written final two hours exmination and receive a grade M3 (0--100). The final grade N is calculated as follows:

(1) If M3 < 50, then N = 1+ (M3 : 20)

(2) If M3 = 50 or M3 > 50, then:

(a) If [(M1 + M2) : 2] > M3, then N = (M1 + M2 + 2 x M3) : 80

(b) If [(M1 + M2) : 2] < (or =) M3, then N = M3 :20.

A possible resit will be evaluated in the same manner as the initial examination.

Retake

Exam:
Written 2 hours
Documentation:
Allowed with restrictions
Calculator:
Not allowed
Evaluation:

Same as ordinary one.

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