MAT-63856 Advanced Applied Logics, 5 cr

Additional information

This course is an extended version of the many-valued logic part of the former Applied Logics course lectured last time in autumn 2011.
It is not possible to include both this course and Applied Logics course to one's curricula. This course will be lectured next time during the academic year 2019-20.
Suitable for postgraduate studies.

Person responsible

Esko Turunen


Implementation Period Person responsible Requirements
MAT-63856 2019-01 1 Esko Turunen
The lecture diary and a passed exam.

Learning Outcomes

Undersanding the role of non classical logics in real life applications. The inreplay of logical systems and various algebraic structures via Lindembaum-Tarski theorem.


Content Core content Complementary knowledge Specialist knowledge
1. Introduction to mathematical fuzzy logic; real life situations where neither black-or-white logic nor statistical methods are applicable.  Graded similarity as a base of fuzzy reasoning. Fuzzy IF-THEN rules. Constructing real world applications by means of multiple valued logic. Para consistent logic in solving decision making problems.    
2. Monoidal Logic as a basis of various non-standard logics: linear logic, intuitionistic logic, basic fuzzy logic, Lukasiewicz logic.  Residuated lattices, Girard monoids, Heyting algebras, BL-algebras, Wajsberg algebras and MV-algebras. Semantics, syntax and completeness of various non-standard logics.   

Instructions for students on how to achieve the learning outcomes

Attendind and take actively part into lessons and excercices, more than 50 points in the final examimation.

Assessment scale:

Numerical evaluation scale (0-5)

Partial passing:

Completion parts must belong to the same implementation

Study material

Type Name Author ISBN URL Additional information Examination material
Lecture slides     Esko Turunen         No   

Additional information about prerequisites
No individual pre-requisites, however, following the course requires a sufficient amount of mathematical thinking from the 1st, 2nd and 3rd year mathematics courses.

Correspondence of content

There is no equivalence with any other courses

Updated by: Turunen Esko, 01.04.2019