Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Selected topics in Mathematical Logic (17.0M507)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Master Academic Studies	Mathematics in Engineering (Year: 1, Semester: Winter)

General information:

Category	Academic-general educative
Scientific or art field	Teorijska i primenjena matematika
ECTS	5

Acquiring fundamental knowledge about mathematical logic and participating in scientific and research work

Knowledge about fundamental notions and results in the field of mathematical logic. Participating in the research in the particular area of logic, based on student`s interests and in cooperation with researchers in the country and abroad.

Basic notions of the syntax of logical systems. Classical logic. Intuitionistic logic. Propositional calculus. Basic notions of the syntax od predicate calculus. Axiomatic (Hilbert’style) system, natural deduction (Gentzen, Prawitz), sequent calculus (Gentzen). Computational interpretation of logic: lambda calculus and the theory of combinators. Curry-Howard correspondence (formulae-as-types, proofs-as-terms) between logical systems, the lambda calculus and the theory of combinators. Basic notions of the semantics of logical systems. DPLL procedure, the tableaux method, the resolution method.

The presentation of the theoretical part during the lecture classes is followed by the characteristic examples which contribute to better understanding of the subject matter. The students are expected to individually study the additional literature which they discuss with the . subject teacher at the consultation classes.

Authors	Title	Year	Publisher	Language
Pierce, B.	Types and Programming Languages	2002	The MIT Press, Massachusetts	English
Barendregt, H.P.	The lambda calculus	1984	North Holland, Amsterdam	English
Barendregt, H.P., Dekkers, W., Statman, R.	Lambda Calculi with Types	2013	Cambridge University Press, Cambridge	English
Sorensen, M.H., Urzyczyn, P.	Lectures on the Curry-Howard Isomorphism	2006	Elsevier, Amsterdam	English
Pierce, B.	Types and Programming Languages	2002	The MIT Press, Massachusetts	English