OVERVIEW

This course provides an introduction to the basics of propositional and first-order predicate logic. The course includes a singificant practical component, to get used to logical and mathematical language, to train logical reasoning, to train the ability of proving simple logical statements, to practice the evaluation of argumentations in natural language.

AIMS AND CONTENT

LEARNING OUTCOMES

Introducing the two basic chapters of classical logic: the logic of propositions and the logic of predicates. Indicating that the study of the correctness of deductions made by specially developed calculation tools accustoms to the appropriate and conscious use of natural language, to the precision and rigor in arguments and helps to organize consistently the discourses and our reasoning activity.

AIMS AND LEARNING OUTCOMES

The aims of the course are to introduce (for 6 credits):

• Deduction and its peculiarity with respect to other forms of reasoning;
• The basis of propositional logic, its syntax and semantics;
• The basis of first-order predicate logic, its syntax and semantics,
• The basic principles of logical formalisation and analysis of natural language sentences and argumentations;
• The methods of semantic tableaux for propositional and predicate logic;
• A logical calculus;
• The notion of first-order theory and model;
• A number of important theorems in logic.

Moreove, the course trains:

• The ability of reading and understanding logical formulas;
• The ability of formalising sentences and argumentations by menas of mathematical logic;
• The ability of assessing argumentations by means of the methods of mathematical logic.
• The ability of proving simple logical theorems.
• The ability to interact collaboratively and to communicate constructively. 
• Collaborative interaction, constructive communication, and dialogical skills.
• Planning skills and the creative approach to the solution of the proposed problems.

For 9 credits, the course introduces also the proof of some of the important theorems of propositional and first-order logic.

At the end of the course, students are supposed to be capable of:

• Understanding the terminology of propositional and predicate logic;
• Understanding the basic concepts of propositional and predicate logic;
• Reading and understanding logical formulas;
• Understanding the concept of first-order theory and model;
• Formalising natural language sentences by means of mathematical logic;
• Assessing argumentations and inferences by means of the logical calculi that we have introduced;
• Proving some simple theorems in logic;
• Understanding the proofs of some of the important theorems in logic (for 9 credits).
• Interacting collaboratively, communicating constructively, engaging effective discussions.
• Creatively approach and plan the solution of the proposed problems.

PREREQUISITES

Students must have attended the first year course on REASONING AND THEORY OF SCIENCE.

TEACHING METHODS

1) Lectures about theory, examples, applications.

2) Exercise and practice sessions, individually and in groups, to train the problem solving skills. 

Attendance is strongly recommended, due to the type of course and to the number of practice moments of the course.

Students are required to register at Aulaweb, where materials useful for the course will be uploaded.

Lecture are hopefully held in presence. Non-attending students are required to contact me to decide the content of the exam and to benefit from further teaching materials. 

 Le lezioni si terranno auspicabilmente in presenza. Chi non frequenta è tenuto a contattare il docente per decidere il programma d'esame e per accedere a materiali didattici aggiuntivi. 

SYLLABUS/CONTENT

Program for 6 credits:

1. introduction to propositional logic:

• Introduction to logic: language and reasoning;
• Types of reasoning: deductive reasoning;
• Propositional logic: syntax and semantics; 
• Truth tables and models;
• Fundamental semantic notions: model, tautology, logical consequence;
• Semantic tableaux for propositional logic;
• Analysis of natural language sentences by menas of propositional logic;
• Analysis of natural language argumentations by means of propositional logic. 
• A logical calculus for propositional logic.
• Soundness and completeness theorems. 

2. Introduction to first-order predicate logic

• The language of first-order predicate logic;
• First-order logic: syntax and semantics;
• Analysis of natural language sentences in first-order logic;
• Semantic tableaux for first-order logic;
• Analysis of argumentations by means of first-order logic;
• A logical calculus for first-order logic;
• First-order theory and first-order models; 
• Soundness and completeness;
• Decidability and complexity.

For 9 credits, besides point 1 and 2: 

• A logical calculus for first-order logic with identity.
• Understanding the proofs of some imporant theorems. 

RECOMMENDED READING/BIBLIOGRAPHY

All required teaching material (lecture notes, slides, etc.) will be made available on Aulaweb or Teams.

Other readins:

• D. Palladino, Corso di Logica, Carocci.

And

• D. Palladino. Logica e teorie formalizzate, Carocci, (Chapter 1.5 for the semantics of first-order logic)
• D. Palladino. Logica e teorie formalizzate, Carocci, (Chapter 1.4 for Hilbert systems)

Or

• E. Mendelson. Introduzione alla logica matematica. Bollati Boringhieri. (Chapter 1 and 2, till 2.4)

The suggest books may change so please contact me before selecting the texts. 

TEACHERS AND EXAM BOARD

Exam Board

DANIELE PORELLO (President)

MARCELLO FRIXIONE

MARIA CRISTINA AMORETTI (Substitute)

LESSONS

LESSONS START

30th  September 2024

EXAMS

EXAM DESCRIPTION

Written exam proposing to solve exercise and approach problems by means of the methods that we have introduced.

Oral exam concerning of the understanding of the topics addressed in the lectures, the logical reasoning skills, and the rational interaction.

Enrollment is mandatory and must be done at least one week before the examination.

ASSESSMENT METHODS

The exam assesses the student's ability to present and to apply the concepts and methods of propositional logic and of first-order predicate logic.

The written part  assesses the ability of using the technical language of logic and the logical methods presented in the course, the ability of analyising natual language arguments, and the ability of proving simple logical theorems. 

The oral part assesses the ability of correctly using the technical language of mathematical logic, the understanding of its main concepts, and the ability of logical reasoning and of rational interaction. 

The evaluation shall depend on the following aspects:

• The basic requirement is the correct and precise use of the technical language of logic;
• The quality of exposition;
• The capacity of applying the methods of propositoinal and first-order logic;
• The capacity of logical reasoning in dialogical interactions.
• The creative approach to problems.

Exam schedule

FURTHER INFORMATION

Attendance is encouraged, due to the practical content of this course. 

Those who cannot attend classes are required to get in touch with the teacher. 

Please do contact the teacher before the exam to assess your practical ability of solving the proposed exercises.