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MODULE DESCRIPTION

Module title Module code Mathematical logic

Lecturer(s) Department where the module is delivered Coordinator: assoc. prof. dr. Stanislovas Norgėla Department of Computer Science Faculty of Mathematics and Informatics Other lecturers: Vilnius University

Cycle Type of the module First Compulsory

Mode of delivery Semester or period when the Language of instruction module is delivered Face-to-face 3 semester Lithuanian

Prerequisites Prerequisites: Discrete mathematics, Algorithm theory.

Number of credits Student‘s workload Contact hours Self-study hours allocated 5 132 68 64

Purpose of the module: programme competences to be developed Purpose of the module is to formalize, analyze knowledge using predicate, modal, and time logics.

Specific competences:  Knowledge and skills of underlying conceptual basis (SK4).  Software development knowledge and skills (SK6).

Learning outcomes of the module: Teaching and learning methods Assessment methods students will be able to - decide if the problem can be solved using methods of mathematical logic - carry out a derivation search in Hilbert type, Gentzen type, semantic tableaux, and resolution methods Test in the middle of - present knowledge using a deductive data- the semester. base and execute the result search of the Problem-oriented teaching, discussions Written examination query at the end of the - determine the complexity of algorithms, semester. which solve a problem, which is presented us- ing formulas of mathematical logic - apply linear temporal logic to analyze plan- ning problems Self-study work: time and Contact hours assignments s k r s r r u o

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Content: breakdown of the topics a c h a y r i

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t Assignments c t u a a m a e t r u t r e s L P T o n - S f b o l a e C L S 1. Introduction. History of logic. Formulas of 4 4 8 6 predicate logic. . Semantics. Formulas satisfiable in infinite set and unsatisfiable in any finite set. 2. Normal prenex forms. Decidable classes. 4 4 8 6 Relation algebra. Formulas with function symbols. 3. Skolemization. Hilbert type predicate calculus. 2 2 4 3 4. Sequent predicate logic calculus. Minus-normal 4 4 8 6 calculus. Intuitionistic logic. Semantic tableaux method. 5. Compactness. Semantic trees. 2 2 4 4 6. Resolution method. Tactics of resolution 2 2 4 3 Study of scientific literature, method. individual problem solving. 7. Deductive databases. Programs with negation 4 4 8 6 operation. Disjunctive Datalog. Semantics of modal logics. 8. Transformation to classical logic. Classification 4 4 8 6 of modal logics. Sequent calculi of modal logics K and S4. Equivalent formulas. Mints theorem. 9. Tableaux method for modal logics K and S4. 2 2 4 4 Classification of temporal logics. CTL logic. 10. Linear temporal logic. Planning problem. 4 4 8 7 Multimodal logics. Hybrid logics. 11. Preparation for the examination and taking 2 4 13 13 hours for preparation, exam. 2 hours for tutorial, 2 hours for exam Total 32 2 32 68 64

Assessment strategy Weight % Deadline Assessment criteria Work during 20 During the Problems are presented to students in every practical training: practical training semester 2 points: if a student correctly solves 75% or more of the problems; 1 point: if a student correctly solves 25% or more but less than 75% of the problems; 0 points: if a student correctly solves less than 25% of the problems. Test 20 During the A test of 8 questions. The value of all the questions is the same. semester 2 points: if 6-8 questions are answered correctly. 1 point: if 2-5 questions are answered correctly. 0 points: if 0-1 questions are answered correctly. Exam 60 Exam An exam consists of 13 problems. The value of every problem is session the same. 6 points: if 12-13 problems are solved correctly. 5 points: if 10-11 problems are solved correctly. 4 points: if 8-9 problems are solved correctly. 3 points: if 6-7 problems are solved correctly. 2 points: if 4-5 problems are solved correctly. 1 point: if 2-3 problems are solved correctly. 0 points: if 0-1 problems are solved correctly. Author Publis Title Number or Publisher or URL hing volume year Required reading S.Norgėla 2007 Logic and artificial intelli- Vilnius, TEV gence (in Lithuanian) S.Norgėla 2004 Mathematical logic (in Vilnius, TEV Lithuanian) Recommended reading R.Lassaigne, M.de Rouge- 1999 Logic and complexity (trans- Vilnius, Žara mont lation in Lithuanian) M.Huth, M.Ryan 2004 Logic in computer science Springer M.Ben-Ari 2003 Mathematical logic for Springer computer science

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