OVERVIEW

This course provides an introduction to the basic principles of propositional and first-order predicate logic, touching also some basic elements of propositional modal logic.

The course includes a singificant practical component, to get used to logical and mathematical language and to train the ability of logical reasoning and of analising argumentations in natural language by means of the methods of mathematical logic. 

AIMS AND CONTENT

LEARNING OUTCOMES

The aims of the course are:

• To introduce the main concepts and techniques of propositional and first-order predicate logic, with particular attention to the practice of analysing argumentations by means of the methods of mathematical logic.
• ​To improve the appropriate technical use of natural language, the precision and rigor in argumentation, the organisation of discourse and the reasoning skills.

AIMS AND LEARNING OUTCOMES

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

• The basis of propositional logic, its syntax and semantics;
• The basis of first-order predicate logic, its syntax and semantics,
• The notion of first-order theory and model;
• The basic principles of logical formalisation and analysis of natural language sentences and argumentations;
• The methods of semantic tableaux for propositional and predicate logic;

Moreove, the course trains:

• The ability of reading and understanding logical formulas;
• The ability of formalising sentence and argumentations by menas of mathematical logic;
• The ability of assessing argumentations by means o the methods of mathematical logic.

For 9 credits, the course introduces also the basics of modal propositional logic and trains the ability of formalising natural languge sentences and argumentations by means of modal logic. 

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

• Understanding the terminology of propositional and predicate logic;
• Understand 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;
• Understanding the basics of modal logic (for 9 credtits)
• Formalising natural language sentences and arguments using modal logic (for 9 credits).

PREREQUISITES

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

TEACHING METHODS

1) Frontal lessons about theory, examples, applications.

2) Exercise and practice sessions. 

Attendance is strongly recommended, due 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, it is however possible to attend the course online on Teams (access codes shall be priovided as soon as possible). 

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;
• 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. 
• Soundness and completeness theorems. 

2. Introduction to first-order predicate logic

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

For 9 credits, besides point 1 and 2: 

3.  Introduction to modal logics:

• Modal logics: syntax and semantics.
• Analysis of modal sentences. 

RECOMMENDED READING/BIBLIOGRAPHY

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

Further readings are:

6 cfu bibliography:

D. Palladino, Corso di logica, Roma, Carocci.

And:

• D. Palladino. Logica e teorie formalizzate, Carocci, (Chapter 1.5, definition of first-order semantics)

or:

• E. Mendelson. Introduzione alla logica matematica. Bollati Boringhieri. (Chapter 1 and 2, and 2.2 for first-order semantics)

 9 cfu: (besides the previous references:

• B. Chellas, Modal Logic: An Introduction, Cambridge: Cambridge University Press. (Chapter 3)

or

• M. Frixione, S. Iaquinto, M. Vignolo. Introduzione alle logiche modali. Laterza. 2016.

TEACHERS AND EXAM BOARD

Exam Board

DANIELE PORELLO (President)

MARCELLO FRIXIONE

MARIA CRISTINA AMORETTI (Substitute)

LESSONS

LESSONS START

28 September 2021

Tuesday 9.00 -- 11.00

Wednesday 9.00 -- 11.00

Thursday 9.00 -- 11.00

Class schedule

LOGIC

EXAMS

EXAM DESCRIPTION

Oral exam concerning the topics addressed in the lectures. 

Written exam proposing to solve simple exercise and to analyse argumentaions in natural language.  

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

ASSESSMENT METHODS

The exam evaluates the student's ability to know and to apply the fundamental concepts of the discipline.

The written part concerns the abiity of approaching simple exercises to assess the abilities of applying the methods presented in the course and to analyise natural language arguments. 

The oral part concerns the theoretical content of the course and assesses the ability of using the technical language of mathematical logic with precision, the understanding of the main concepts of propositional and predicate logic (and modal logic, for 9 credits), and the ability of reasoning logically. 

Exam schedule

FURTHER INFORMATION

Those who cannot attend classes are required to get in touch with the teachers. Please do contact the teacher before the exam to assess your practical ability of solving the proposed exercises.