Learning outcomes of the course unit
1-knowing and comprehension capability
analytical competence in relation to the logical system considered.
2 -knowing and applied comprehension capabilities
Application of logical techniques in the 'translation' of natural language
statements and arguments in the symbolic system.
3-4-5 independent judgment, communicative skills, learning capabilities
Ability to learn the method of demonstration. Ability to develop demonstrations
on their own.
There are no prerequisites.
Course contents summary
The aim of the course is to provide an understanding of the logic of propositions and predicates. The presentation is in natural deduction style. After providing some historical elements, I introduce the languages and derivation procedures. Particular importance will be given to the discovery of proof..
The origins of logic as deductive system, historical elements; Aristotelian and Stoic logic, the logic of consequences (outline)
- presentation of a logical system in the style of natural deduction
- The propositional calculus:
rules of introduction / elimination of connectives
disjunction elimination rule
rule of reduction to absurdity
conditional proof rule
demonstrations of sequences and theorems
syntax of the propositional calculation
the consistency and completeness of the propositional calculus
- logic of predicates
Translation of natural language phrases into the logical one
rules for introducing / eliminating quantifiers
models, definition of truth
the consistency and completeness of the propositional calculation
Manual: E.J. Lemmon, Elements of logic, Laterza
additional reference material at: http:
/ / www.slprbo.unipr.it (folder 'documents') and password to the User
Students enrolled in the course
F.B. Fitch, Symbolic Logic, New York 1951
E.J. Lemmon, Beginning logic, London 1965
B. Mates, Elementary logic, New York 1965
M. E. Szabo, Collected Papers of Gerhard Gentzen, North-Holland, 1969
P. Suppes, Introduction to logic, Princeton 195
Assessment methods and criteria
final written test: it consists of a series of questions / exercises designed to test the learning and understanding of the topics.
Particular attention will be paid to: 1) the understanding of proofs, 2) ability to use a symbolic language; 3) cleaning in the presentation of the exercises.
Non-attending students are required to know the manual and read the additional bibliographic material