Menù principale
B020988 - ADVANCED TOPICS IN LOGIC
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2020-21
Course year
First year - Second Semester
Belonging Department
Humanities (DILEF)
Course Type
Single education field course
Scientific Area
M-FIL/02 - LOGIC AND PHILOSOPHY OF SCIENCE
Credits
12
Teaching Hours
72
Teaching Term
22/02/2021 ⇒ 28/05/2021
Attendance required
Yes
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Teaching Language
Italian.
Course Content
Introduction to Proof Theory
Suggested readings (Search our library's catalogue)
1) Lecture notes by the instructor (accessible online), with a reference
list;
2) for a deeper understanding of several topics touched in the lectures,
see:
(i) J.Y.Girard, Proof Theory and Logical Complexity, Napoli 1987;
(ii) A.S.Troelstra, H.Schwichtenberg, Basic Proof Theory, Cambridge 2000
(2nd ed.);
(iii) S.Negri and J. von Plato, Structural Proof Theory, Cambridge 2001;
(iv) M.H.Sorensen, P.Urczyn, Lectures on the Curry-Howard Isomorphism,
Amsterdam-New York 2006;
(iii) H.Schwichtenberg, S.S.Wainer, Proofs and Computations, Cambridge
2012.
list;
2) for a deeper understanding of several topics touched in the lectures,
see:
(i) J.Y.Girard, Proof Theory and Logical Complexity, Napoli 1987;
(ii) A.S.Troelstra, H.Schwichtenberg, Basic Proof Theory, Cambridge 2000
(2nd ed.);
(iii) S.Negri and J. von Plato, Structural Proof Theory, Cambridge 2001;
(iv) M.H.Sorensen, P.Urczyn, Lectures on the Curry-Howard Isomorphism,
Amsterdam-New York 2006;
(iii) H.Schwichtenberg, S.S.Wainer, Proofs and Computations, Cambridge
2012.
Learning Objectives
(i) Knowledge and understanding. Knowledge of the main theoretical issues and methodologies in structural proof theory, combinatory logic, (typed/untyped) lambda calculus. Understanding specific problems in these areas.
(ii) Applying knowledge and understanding. Applying the above knowledge and understanding though suggested exercises dealing with specific problems in the areas of logic and philosophy of logic.
(iii) Making judgements.
Critical understanding of scientific contributions (articles, books) in an autonomous way.
(iv) Communication skills.
Ability to present in an appropriate way problems, solutions to problems, theories, arguments, proofs.
(ii) Applying knowledge and understanding. Applying the above knowledge and understanding though suggested exercises dealing with specific problems in the areas of logic and philosophy of logic.
(iii) Making judgements.
Critical understanding of scientific contributions (articles, books) in an autonomous way.
(iv) Communication skills.
Ability to present in an appropriate way problems, solutions to problems, theories, arguments, proofs.
Prerequisites
An introduction to Logic (12 CFU), BA in Philosophy or equivalent study. A preliminary contact with the instructor is advisable, in order to evaluate the background vis a vis.
Teaching Methods
Lectures, plus tutorial and exercises under the guidance of the instructor.
Further information
Course materials (lectures notes, exercises etc.) will be available online at the Moodle page of the course.
The course requires a regular attendance (at least 2/3 of the lectures).
The course requires a regular attendance (at least 2/3 of the lectures).
Type of Assessment
Oral examination, 45 minutes, three questions: it is aimed at witnessing
an adequate mastering of (i) the basic theoretical notions and disciplinary
lexicon, (ii) the logical techniques needed to solve exercises;(iii) some
proof among those of the main results.Emphasis is put on adequate
knowledge in Gentzen's formalisms.
The grading is obtained by a simple average over the marks assigned to
the single answers.
an adequate mastering of (i) the basic theoretical notions and disciplinary
lexicon, (ii) the logical techniques needed to solve exercises;(iii) some
proof among those of the main results.Emphasis is put on adequate
knowledge in Gentzen's formalisms.
The grading is obtained by a simple average over the marks assigned to
the single answers.
Course program
1) Additional topics in propositional and predicative classical logic:
normal forms, theorems of Herbrand and Skolem; monadic logic.
2) Introduction to proof theory. Gentzen's sequent calculi. Proof of
the Hauptsatz. Application: the interpolation theorem via Maehara's
lemma.
3) Hauptsatz and abstraction: the consistency of Grishin's naive set
theory.
4) Introduction to typed lambda calculus. Basic notions and fundamental
properties. Proof of strong normalization.
normal forms, theorems of Herbrand and Skolem; monadic logic.
2) Introduction to proof theory. Gentzen's sequent calculi. Proof of
the Hauptsatz. Application: the interpolation theorem via Maehara's
lemma.
3) Hauptsatz and abstraction: the consistency of Grishin's naive set
theory.
4) Introduction to typed lambda calculus. Basic notions and fundamental
properties. Proof of strong normalization.