The course aims to provide knowledge of classical logic (propositional and first order), intuitionistic logic and modal logic. Will also be treated: i) deductive and semantic methods; ii) completeness results; iii) limiting results. At the end of the course the student must demonstrate that he has the necessary knowledge to reason with a formal logical system, both in a classical context and in an intuitionist or modal context. Knowing how to transfer the theoretical notions learned in logical informatic contexts, such as the type theory. This knowledge will allow the student to: i) carry out formal proofs with a deductive system; ii) handling semantical notions for the refutation of logical formulas; iii) reasoning with axiomatic systems. At the end of the course the student will be able to: i) compare logical systems, ie classics, intuitionists and modals reasoning both syntactically (deductive systems) and semantically (models); continue the studies autonomously within the logic of computer science.
1)Propositional logic:
-propositions and connectives
-semantics
-natural deduction
-soundness and completeness
2)Predicate logics:
-quantifiers
-structures
-similarity types
-semantics
-identity
-natural deduction
-soundness and completeness
3)basic model theory
-equivalence, isomporphism, categoricity
4) Peano Arithmetic
-first and second incompleteness theorems
| Author | Title | Publisher | Year | ISBN | Note |
| van Dalen, Dirk | Logic and Structure. (Edizione 5) | Springer | 2013 | 978-1-4471-4557-8 |
Oral examination (about 15/20 minutes of interrogation)
In order to pass the exam, the student must have sufficient knowledge of all the subjects (including the proofs of the theorems).
Better is the knowledge of course topics, better is the result of exam.
