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Mathematical Logic

ОК.14

Обов’язкова дисципліна для ОП

First

2022/2023

3 Semester

6

LO 1. Apply the knowledge about basic forms and laws of abstract logical thinking, foundations of scientific cognition methodology, forms and methods of extracting, analyzing, processing and synthesizing information in computer science. LO 5. Design, develop and analyze algorithms for solving computational and logical problems. Evaluate algorithms efficiency and complexity on the basis of formal models of algorithms and computable functions.

Distance form

Know: basic concepts of discrete mathematics: basics of set theory, relations theory, Boolean function theory. Be able to: establish basic set-theoretic relations, use the apparatus of Boolean function theory.

The goal of the discipline is to acquire fundamental knowledge in the basics of the mathematical logic, which includes studying semantic models and formal languages of logic, exploring their capabilities for describing subject areas. It also involves the study of formal-axiomatic logical systems and proof-search systems, as well as understanding their applications in practical domains. The educational discipline "Mathematical Logic" is a component of the educational professional program "Informatics" of the first (bachelor) level of higher education in the field of knowledge 12 "Information Technologies" from the specialty 122 "Computer Science". This discipline is a compulsory course in the "Informatics" program. It is taught in the 3rd semester of the 2nd course in the amount of 180 hours (6 ECTS credits), in particular: lectures – 56 hours, practical classes – 28 hours, consultations – 2 hours, independent work – 94 hours. The course includes 3 midterm exam. The discipline ends with an exam in the 3rd semester.

1. Nikitchenko M.S., Shkilniak S.S. Matematychna lohika ta teoriia alhorytmiv. – К., 2008. 2. Nikitchenko M.S., Shkilniak S.S. Prykladna lohika. – K., 2013. 3. Shkilniak S.S. Matematychzna lohika: pryklady i zadachi. – К., 2022. 4. Belnap N., Steel T. The logic of questions and answers. – Yale Univ. Press, 1976. 5. Boolos G., JeffreyR. Computability and Logic. – Cambridge University Press, 1989. 6. Chang Ch.-L, Lee R. Symbolic Logic and Mechanical Theorem Proving, – Academic Press, 1973. 7. Gabbay D. Elementary Logic (A procedural perspective). – Prentice Hall Europe, 1998. 8. Kleene S.C. Mathematical Logic. – Dower Publications, 2013. 9. Kröger F., Merz S. Temporal logic and state systems. – Berlin-Heidelberg: Springer-Verlag, 2008. 10. Mendelson E. Introduction to Mathematical Logic. 6th ed. – CRC Press, 2015. 11. Shoenfield J. Mathematical Logic. – Addison-Wesley Publishing company, 1967.

Lectures, practical classes, independent work.

Semester Assessment (by levels): 1. Midterm Exam 1: LO 1.1, LO 2.1, LO 2.2 – 6 points 2. Midterm Exam 2: LO 1.1, LO 2.1 – 16 points 3. Midterm Exam 3: LO 1.2, LO 1.3, LO 2.2 – 14 points 4. Homework Assignments 1: LO 1.1, LO 1.2, LO 2.2, LO 3.1 – 5 points 5. Homework Assignments 2: LO 1.1, LO 2.1, LO 3.1 – 8 points 6. Homework Assignments 3: LO 1.2, LO 1.3, LO 2.2, LO 3.1 – 7 points 7. Students' work in classes: LO 3.1 – 4 points. Final Assessment (in the form of an exam): – maximum number of points that can be obtained by the student: 40 points; – earning outcomes to be evaluated: LO 1.1, LO 1.2, LO 1.3, LO 2.1, LO 2.2; – form of examination and types of tasks: written exam.

Ukrainian