
Course unit
LOGIC
SC02105452, A.A. 2016/17
Information concerning the students who enrolled in A.Y. 2016/17
ECTS: details
Type 
ScientificDisciplinary 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 
Hours of Individual study 
Shifts 
Practice 
2.0 
18 
32.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
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)
BONOTTO
CINZIA
(Supplente)
MASCHIO
SAMUELE
(Supplente)
SAMBIN
GIOVANNI
(Supplente)

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 (GĂ¶del) 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.


