Mathematical Logic

Lecturer:

Alena Šolcová (gar.)

Tutor:

Alena Šolcová (gar.), Karel Klouda, Petr Matyáš

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

2. Semantic consequence and semantic equivalence. Lindenbaum algebra of propositional logic formulas. Boolean algebra. CNF and DNF. Karnaugh maps. Boolean function minimization.

3. Basic concepts of the resolution algorithm in propositional logic. Formalizing natural language sentences, inadequacy of propositional logic. Syntax of predicate logic.

4. Semantics of predicate logic. Construction of simple models in predicate logic language.

5. Semantic consequence in predicate logic. Satisfiability. Semantic consequence problem, algorithmic point of view.

6. Formalizing natural language sentences in predicate logic. Syntactic derivation in propositional and predicate logic. Construction of successful tableaus.

7. Other logics used in CS.

Syllabus of tutorials:

1. Formalization of simple statements. Truth tables, time complexity of their processing. Semantic consequence and semantic equivalence. CNF and DNF. Syntax and semantic of predicate logic. Resolution method in propositional logic.

2. Formalization of natural language sentences. Syntax of predicate logic. Semantic of predicate logic. Construction of simple models in predicate logic language. Semantic consequence in predicate logic. Satisfiability. Semantic consequence problem, algorithmic point of view. Proofs in propositional and predicate logic. Tableau method.

Study Objective:

Study materials:

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Informtion Systems and Management (Presented in Czech) (compulsory course in the program)
• Information Technology (Presented in Czech) (compulsory course in the program)
• Computer engineering (Presented in Czech) (compulsory course in the program)
• Software engineering (Presented in Czech) (compulsory course in the program)
• Computer Science (Presented in Czech) (compulsory course in the program)
• Web and Multimedia (Presented in Czech) (compulsory course in the program)
• Informatics - Plan for Period Before Assignement of Specialization (Presented in Czech) (compulsory course in the program)