Mathematical Logic

Code	Completion	Credits	Range	Language
BI-MLO	Z,ZK	5	2+1.5	Czech

Lecturer:

Kateřina Trlifajová (gar.), Alena Šolcová

Tutor:

Kateřina Trlifajová (gar.), Zdeněk Konfršt, Marta Nollová, Alena Šolcová, Daniel Vašata

Supervisor:

Department of Applied Mathematics

Synopsis:

Students have knowledge of the syntax and semantics of the propositional and predicate logic. They master the Boolean algebra, both theoretically as an instance of universal algebra, and practically as a tool to describe the world of digital systems. They get skills to handle Boolean functions, normal forms, maps, and minimisation methods needed in the further modules.

Requirements:

Syllabus of lectures:

1. Informal logic as the language of mathematics. Ambiguity of natural languages. Languages nad metalanguages. Formal languages.

2. Language of propositional logic, syntax and semantics. Truth tables, time complexity of their processing.

3. Semantic consequence and semantic equivalence. Lindenbaum algebra of propositional logic formulas. Boolean algebra.

4. CNF and DNF. Karnaugh maps. Boolean function minimization.

5. Basic concepts of the resolution algorithm in propositional logic.

6. Formalizing natural language sentences, inadequacy of propositional logic. Syntax of predicate logic.

7. Semantics of predicate logic.

8. Construction of simple models in predicate logic language.

9. Semantic consequence in predicate logic. Satisfiability.

10. Semantic consequence problem, algorithmic point of view.

11. Formalizing natural language sentences in predicate logic.

12. Syntactic derivation in propositional and predicate logic. Construction of successful tableaus.

13. Other logics used in CS.

Syllabus of tutorials:

1. Formalization of simple statements.

2. Truth tables, time complexity of their processing.

3. Semantic consequence and semantic equivalence.

4. CNF and DNF.

5. Resolution method in propositional logic.

6. Formalization of natural language sentences. Syntax of predicate logic.

7. Syntax and semantic of predicate logic.

8. Semantic of predicate logic.

9. Construction of simple models in predicate logic language.

10. Semantic consequence in predicate logic. Satisfiability.

11. Semantic consequence problem, algorithmic point of view.

12. Proofs in propositional and predicate logic. Tableau method.

Study Objective:

Study materials:

Note:

Time-table for winter semester 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon	roomT9:302 Konfršt Z. 09:15–10:45 ODD WEEK (lecture parallel2 parallel nr.207) Dejvice NBFIT učebnaroomT9:344 Konfršt Z. 11:00–12:30 EVEN WEEK (lecture parallel2 parallel nr.205) Dejvice NBFIT ucebnaroomT9:344 Vašata D. 12:45–14:15 ODD WEEK (lecture parallel2 parallel nr.208) Dejvice NBFIT ucebna roomT9:302 Konfršt Z. 09:15–10:45 EVEN WEEK (lecture parallel2 parallel nr.210) Dejvice NBFIT učebnaroomT9:344 Konfršt Z. 11:00–12:30 ODD WEEK (lecture parallel2 parallel nr.206) Dejvice NBFIT ucebnaroomT9:344 Vašata D. 12:45–14:15 EVEN WEEK (lecture parallel2 parallel nr.211) Dejvice NBFIT ucebna
Tue	roomT9:346 Šolcová A. 09:15–10:45 EVEN WEEK (lecture parallel1 parallel nr.112) Dejvice NBFIT učebnaroomT9:346 Trlifajová K. 11:00–12:30 ODD WEEK (lecture parallel1 parallel nr.102) Dejvice NBFIT učebnaroomT9:344 Trlifajová K. 12:45–14:15 EVEN WEEK (lecture parallel1 parallel nr.109) Dejvice NBFIT ucebna roomT9:346 Trlifajová K. 09:15–10:45 ODD WEEK (lecture parallel1 parallel nr.113) Dejvice NBFIT učebnaroomT9:346 Trlifajová K. 11:00–12:30 EVEN WEEK (lecture parallel1 parallel nr.105) Dejvice NBFIT učebnaroomT9:302 Vašata D. 12:45–14:15 ODD WEEK (lecture parallel1 parallel nr.114) Dejvice NBFIT učebna roomT9:302 Vašata D. 12:45–14:15 EVEN WEEK (lecture parallel2 parallel nr.214) Dejvice NBFIT učebna
Fri	roomT9:344 Šolcová A. 07:30–09:00 EVEN WEEK (lecture parallel2 parallel nr.202) Dejvice NBFIT ucebnaroomT9:105 Trlifajová K. 09:15–10:45 (lecture parallel1) Dejvice Posluchárna roomT9:344 Šolcová A. 07:30–09:00 ODD WEEK (lecture parallel2 parallel nr.209) Dejvice NBFIT ucebnaroomT9:344 Šolcová A. 09:15–10:45 EVEN WEEK (lecture parallel2 parallel nr.203) Dejvice NBFIT ucebna roomT9:344 Šolcová A. 09:15–10:45 ODD WEEK (lecture parallel2 parallel nr.204) Dejvice NBFIT ucebna
Thu	roomT9:105 Šolcová A. 07:30–09:00 (lecture parallel2) Dejvice PosluchárnaroomT9:302 Nollová M. 09:15–10:45 EVEN WEEK (lecture parallel1 parallel nr.106) Dejvice NBFIT učebnaroomT9:301 Nollová M. 11:00–12:30 EVEN WEEK (lecture parallel1 parallel nr.107) Dejvice NBFIT učebnaroomT9:346 Nollová M. 14:30–16:00 ODD WEEK (lecture parallel1 parallel nr.101) Dejvice NBFIT učebnaroomT9:346 Nollová M. 16:15–17:45 ODD WEEK (lecture parallel1 parallel nr.103) Dejvice NBFIT učebna roomT9:346 Vašata D. 14:30–16:00 EVEN WEEK (lecture parallel1 parallel nr.104) Dejvice NBFIT učebna
Fri	roomT9:346 Vašata D. 07:30–09:00 ODD WEEK (lecture parallel2 parallel nr.212) Dejvice NBFIT učebnaroomT9:302 Nollová M. 11:00–12:30 EVEN WEEK (lecture parallel1 parallel nr.108) Dejvice NBFIT učebnaroomT9:347 Nollová M. 12:45–14:15 ODD WEEK (lecture parallel1 parallel nr.110) Dejvice NBFIT učebna roomT9:346 Vašata D. 07:30–09:00 EVEN WEEK (parallel nr.213) Dejvice NBFIT učebnaroomT9:302 Nollová M. 11:00–12:30 ODD WEEK (lecture parallel1 parallel nr.111) Dejvice NBFIT učebnaroomT9:347 Nollová M. 12:45–14:15 EVEN WEEK (lecture parallel2 parallel nr.201) Dejvice NBFIT učebna roomT9:302 Nollová M. 07:30–09:00 ODD WEEK (parallel nr.215) Dejvice NBFIT učebna

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

Computer Science, Version for Students who Enrolled in 2009 and 2010, Presented in Czech (compulsory course in the program)
Computer engineering, Version for Students who Enrolled in 2009 and 2010, in Czech (compulsory course in the program)
Software Engineering, Version for Students who Enrolled in 2009 and 2010, in Czech (compulsory course in the program)
Web and Multimediac, Version for Students who Enrolled in 2009 and 2010, Presented in Czech (compulsory course in the program)
Information Systems and Management, Version for Students who Enrolled in 2009 and 2010, in Czech (compulsory course in the program)
Information Technology, Version for Students who Enrolled in 2009 and 2010, Presented in Czech (compulsory course in the program)
Informatics, Version for Students who Enrolled in 2009 and 2010, Presented in Czech (compulsory course in the program)
Informatics (Bachelor)- Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
Information Systems and Management - Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
Information Technology- Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
Computer Engineering, Version for those who Enrolled in 2011 and 2012, in Czech (compulsory course in the program)
Software Engineering- Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
Computer Science - Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
Web and Multimedia- Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)