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Second cycle
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School of Science
Course unit
SC02105452, A.A. 2016/17

Information concerning the students who enrolled in A.Y. 2016/17

Information on the course unit
Degree course First cycle degree in
SC1167, Degree course structure A.Y. 2011/12, A.Y. 2016/17
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination LOGIC
Website of the academic structure
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge MARIA EMILIA MAIETTI MAT/01

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/01 Mathematical Logic 6.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 2.0 18 32.0 No turn
Lecture 4.0 32 68.0 No turn

Start of activities 01/10/2016
End of activities 20/01/2017
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
6 a.a 2018/2019 01/10/2018 28/02/2020 MAIETTI MARIA EMILIA (Presidente)
CIRAULO FRANCESCO (Membro Effettivo)
5 a.a. 2017/2018 01/10/2017 28/02/2019 MAIETTI MARIA EMILIA (Presidente)
CIRAULO FRANCESCO (Membro Effettivo)
MASCHIO SAMUELE (Membro Effettivo)
SAMBIN GIOVANNI (Membro Effettivo)

Prerequisites: None.
Target skills and knowledge: The aim of the course is to provide an introduction to logic and its relevance to mathematics and computer science. In particular, the student will be able to express a sentence via a formula in a formal language, to give a proof via a derivation in an axiomatic system and to give counterexamples when a formula is not derivable. Moreover, the student will be helped to understand some general concepts, such as language, expression, proposition, assertion, metalanguage, and some concepts specific to mathematics, such as derivation, proof, axiomatic system, induction, independence, interpretation. The student will be led to master such concepts and to distinguish and apply them in mathematics and in common life. The course will show how logic clarifies in a rigorous way the intrinsic limits to what a language can express and to what one can prove in a given axiomatic system. Finally, the course will give some hystorical information about logic, its potentialities and its future perspectives.
Examination methods: Written examination
Course unit contents: 1. Language, sign and expression, symbol and proposition, assertion and declaration, metalanguage, reference levels, infinite iteration.

2. Notion of machine or robot, meaning of connectives and their
deductive rules, resource logics, structural rules, intuitionistic logic, classical logic, truth tables, propositional functions and subsets, quantifiers and their deductive rules.

3. Decision methods for propositional classical sequent calculi.

4. Detailed analysis of a concrete example, natural numbers and axiomatic theory of Peano Arithmetic, abstract algebraic structures.

5. Definition and proof by induction, term and formula, interpretation of formulas, validity.

6. Sketch of completeness and incompleteness (Gödel) theorems and of indecidability (Church) and their meaning
Planned learning activities and teaching methods: Beside lectures on theory, the teacher will assign many exercises and will correct their solution. There will be simulations of written exams.
Additional notes about suggested reading: The teacher will provide written notes including all the necessary theoretical and practical aspects of each topic treated in the course.
Textbooks (and optional supplementary readings)
  • Maria Emilia Maietti, Manuale pratico di Logica. --: Padova, 2016. dispense
  • Giovanni Sambin, Per istruire un robot. --: Libreria Cortina, Padova, 2007.