The course consists of two parts: a general part containing an introduction to formal logic; and a specific part containing an introduction to Proof Theory. The course focuses on the analysis of the concept of decidability in formal theories.

The course will focus on the following topics:

01.01 Arguments and logical fallacies;

02 Propositional Logic;

02.01 Syntax of Propositional Logic;

02.02 Semantics of Propositional Logic;

03 First Order Logic;

03.01 Syntax of the First Order Logic;

03.02 Semantics of the First Order Logic;

04 Metatheory of formal systems;

04.01 Consistency; Completeness; Decidability;

05 Mathematical Logic and Computability Theory;

05.01 The concept of algorithm;

05.02 Functions and Computability;

05.03 Turing Machines;

05.04 Undecidable problems;

06 Computability, logic and foundations of mathematics;

06.01 Gödel's Theorems.

There are no strict pre-requisites for this course, but a basic introduction to Logic might provide a useful background.

Knowledge and understanding

After the course students should be able to understand and explain texts by history of logic, discuss some of the classical problems in mechanization of reasoning and philosophy of computing, use the bibliographical tools and repertories available in this field.

Applying knowledge and understanding

After the course students should be able to discuss and evaluate various claims and arguments both in the specialistic debate and in the general contemporary cultural debate.

Making judgements

After the course students should be able to make autonomous and original judgements about the arguments in the debate. To this end discussions in the classroom will be encouraged. Originality and autonomous judgement will be part of the final evalution of the student's performance

Communication skills

After the course students should be able to explain and discuss the relevant topics with conceptual and linguistic exactness, and to offer efficacious  and synthetic accounts of the subject matter. To this end, verbal interaction in the classroom and a careful reading and analysis of the relevant texts will be encouraged

Learning skills

After the course students should be acquainted with the subject matter and the method of research enough to be able to proceed on their own  in gathering further knowledge from the literature in the field and in contiguous fields. To this end they should also improve their ability to read English texts in the field.

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

Lectures:

Training Camp: https://filosofia.uniurb.it/training-camp/

Synergia Lectures: https://sites.google.com/a/uniurb.it/synergia

Lectiones Commandinianae: https://sites.google.com/site/lectionescommandinianae/

Teaching

Classroom lectures offering general frameworks, analyses of particular topics and exercises, comments to the relevant literature. Before, during and after the lecture questions, comments and discussions by the students are encouraged. Of course personal study at home will be equally important.

Attendance

Students should attend classes regularly and actively, since the very beginning. Because of the analytic and often abstract character of the subject matter, active participation in classroom discussion will be very useful. In order to do that, and in general to follow the lectures successfully, it is strongly advised to do every day the homework suggested as preparation for the following lecture.

For the students of the curriculum Philosophy and History of Science, this course constitutes one part of a bigger course which includes the course in Information Technology. In order to receive the grade for the whole course, a student must complete both courses. His/her evaluation will be based on the evaluation received in both courses. In addition, the student will have to prepare an essay between 2.000 and 4.000 words on a topic agreed with both lecturers. The essay must be submitted at least 7 days prior to the examination of the first component of the course chosen by the student. The essay will also be graded by the lecturers and such grade constitutes an integral part of the whole grade.

Course books

Richard L. Epstein, “An Introduction to Formal Logic”, Advanced Reasoning Forum, 2016.

Additional texts will be given to students during the lectures (the additional texts will also be available on the Moodle platform › blended.uniurb.it).

Assessment

Written and oral examination. You will be asked to analyze concepts, solve exercises and demonstrate theorems.
This dual-mode makes it possible to assess, in the best way, the achievement of the established formative objectives and competencies.
The final evaluation will take into account the knowledge acquired by the student in terms of analysis of concepts, definitions, theorems, problems, theories, techniques, methods, scientific instruments, etc. The student's ability to use conceptual tools to solve problems and prove/analyze theorems and active participation in the classroom will also contribute to the final evaluation. Finally, the student's capacity for rigorous analysis of themes and problems, autonomy in solving problems and proving theorems, personal and autonomous reworking of knowledge, and planning will be particularly well-appreciated.

All these elements will have equal weight in the assessment. They will be well distinguished on a scale of four levels (not sufficient, sufficient, good, excellent).
The final mark will be expressed on a range from 18/30 to 30/30. A sufficiently rigorous and clear exposition -using adequately specific terms- of the basic contents, concepts, methods, and the ability to solve simple exercises and prove simple theorems will be enough to obtain a sufficient evaluation and to pass the examination (18/30). The other marks will be calibrated on this basis.

For the students of the curriculum Philosophy and History of Science, this course constitutes one part of a bigger course which includes the course in Information Technology. In order to receive the grade for the whole course, a student must complete both courses. His/her evaluation will be based on the evaluation received in both courses. In addition, the student will have to prepare an essay between 2.000 and 4.000 words on a topic agreed with both lecturers. The essay must be submitted at least 7 days prior to the examination of the first component of the course chosen by the student. The essay will also be graded by the lecturers and such grade constitutes an integral part of the whole grade.

Disabilità e DSA

Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.

A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.

Teaching

They will study on their own (individually or with others) according to the directions of this vademecum and if possible with the help which can be given by the teacher during office hours or through e-mail, Skype, etc.

Attendance

In order to make up for the impossibility of attending classes, a hard and careful study is required. One should already possess good skills of autonomous learning and some capacity to read and understand logic and philosophical texts, at least at a basic level. Whenever possible, it is advisable to work with other students. 

For the students of the curriculum Philosophy and History of Science, this course constitutes one part of a bigger course which includes the course in Information Technology. In order to receive the grade for the whole course, a student must complete both courses. His/her evaluation will be based on the evaluation received in both courses. In addition, the student will have to prepare an essay between 2.000 and 4.000 words on a topic agreed with both lecturers. The essay must be submitted at least 7 days prior to the examination of the first component of the course chosen by the student. The essay will also be graded by the lecturers and such grade constitutes an integral part of the whole grade.

Course books

Richard L. Epstein, “An Introduction to Formal Logic”, Advanced Reasoning Forum, 2016.

Additional texts will be given to students during the lectures (the additional texts will also be available on the Moodle platform › blended.uniurb.it).

Non-attending students are invited to contact the professor with regard to the additional texts.

Assessment

Written and oral examination. You will be asked to analyze concepts, solve exercises and demonstrate theorems.
This dual-mode makes it possible to assess, in the best way, the achievement of the established formative objectives and competencies.
The final evaluation will take into account the knowledge acquired by the student in terms of analysis of concepts, definitions, theorems, problems, theories, techniques, methods, scientific instruments, etc. The student's ability to use conceptual tools to solve problems and prove/analyze theorems will also contribute to the final evaluation. Finally, the student's capacity for rigorous analysis of themes and problems, autonomy in solving problems and proving theorems, personal and autonomous reworking of knowledge, and planning will be particularly well-appreciated.

All these elements will have equal weight in the assessment. They will be well distinguished on a scale of four levels (not sufficient, sufficient, good, excellent).
The final mark will be expressed on a range from 18/30 to 30/30. A sufficiently rigorous and clear exposition -using adequately specific terms- of the basic contents, concepts, methods, and the ability to solve simple exercises and prove simple theorems will be enough to obtain a sufficient evaluation and to pass the examination (18/30). The other marks will be calibrated on this basis.

For the students of the curriculum Philosophy and History of Science, this course constitutes one part of a bigger course which includes the course in Information Technology. In order to receive the grade for the whole course, a student must complete both courses. His/her evaluation will be based on the evaluation received in both courses. In addition, the student will have to prepare an essay between 2.000 and 4.000 words on a topic agreed with both lecturers. The essay must be submitted at least 7 days prior to the examination of the first component of the course chosen by the student. The essay will also be graded by the lecturers and such grade constitutes an integral part of the whole grade.

Disabilità e DSA

Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.

A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.

Foreign students will be allowed to use English for questions and comments during the class, for all the required readings, and for the final examination.

For the students of the curriculum Philosophy and History of Science, this course constitutes one part of a bigger course which includes the course in Information Technology. In order to receive the grade for the whole course, a student must complete both courses. His/her evaluation will be based on the evaluation received in both courses. In addition, the student will have to prepare an essay between 2.000 and 4.000 words on a topic agreed with both lecturers. The essay must be submitted at least 7 days prior to the examination of the first component of the course chosen by the student. The essay will also be graded by the lecturers and such grade constitutes an integral part of the whole grade.