# Logic [Matricole pari] (2020/2021)

Course code
4S00084
Name of lecturer
Andrea Masini
Coordinator
Andrea Masini
Number of ECTS credits allocated
6
INF/01 - INFORMATICS
Language of instruction
Italian
Location
VERONA
Period
I semestre dal Oct 1, 2020 al Jan 29, 2021.

#### Learning outcomes

The class offers an introduction to logic as a tool for rational inquiry and abstract thinking, and as a foundation of computer science. Students get exposure to logical languages, learning how to understand, express, and connect concepts in this languages. Students learn how to build models and proofs of logical formulae in one or more deductive systems. They acquire the skills to understand, formulate, and assess formal arguments expressed in one or more logics, as well as the preparation to pursue further studies in artificial intelligence and theory of computing.

#### Syllabus

Mathematical Notions
Sets, relations, functions.
Equivalence relations, Ordering relations.
Natural Numbers and induction.
Cardinality.

Propositional Logic
Propositions and Connectives,
Semantics,
Natural Deduction,
Soundness, Completeness

PredicateLogic
Quantifiers
Structures
The Language of a Similarity Type
Semantics,
Identity,
NaturalDeduction
Soundness, Completeness
Natural Deduction and Identity

Formalisation of properties in predicate logic
Properties and functions for natural numbers e.g.:
“n is a prime numbers”, “m is the sum of two natural numbers”, etc.
Mathematical theories

 Author Title Publisher Year ISBN Note van Dalen, Dirk Logic and Structure. (Edizione 5) Springer 2013 978-1-4471-4557-8

#### Assessment methods and criteria

The exam consists of two parts.
Part I:
Multiple choice test with 20 yes-no questions. A final score of at least 10 is required to pass the test. The final score is obtained by summing up the numerical evaluation of each answers assigned as follows: 1 for every correct answer, -0.5 for every incorrect answer, 0 for no answer.
Part II:
Only students who pass Part I can access this part. This consists of a written test with 6 open questions on theorems, proofs and exercises related to the topics covered by the lectures.
A score of 6 is assigned to each correct answer. A final score exceeding 30 is eligible for a cum laude qualification.