N_MaL Mathematical Logic

University of Finance and Administration
Winter 2012
Extent and Intensity
1/1. 3 credit(s). Type of Completion: z (credit).
Teacher(s)
prof. PhDr. Vladimír Čechák, CSc. (seminar tutor)
Guaranteed by
prof. PhDr. Vladimír Čechák, CSc.
Department of Computer Science and Mathematics – Departments – University of Finance and Administration
Contact Person: Dagmar Medová, DiS.
Timetable of Seminar Groups
N_MaL/vAPH: Fri 9. 11. 12:00–13:30 S13, Sat 1. 12. 9:45–11:15 S14, 11:30–13:00 S14, V. Čechák
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course objective is introducing students into the construction of statement logic and predicate logic. The elementary statement logic is outlined as a special case of binary arithmetic and the analogy with Boolean algebra is studied. In introductory lectures we will pay attention to functional completeness of statement logic and to selected aspects of some applications. Then it will be the construction of axiomatic systems of statement logic (with the consideration of using functional completeness knowledge). The analysis of basic characteristics of axiomatic systems (completeness, axiom independence, indisputability) will be lectured and their use in logic analysis of axiomatic theories. The problems of conjunctive and disjunctive normal forms are also a part of lectures as well as the range of predicate logic including axiomatic issues, and the use of predicate logic devices to a formalization of “beyond logic” theories. The lectures will be concluded by prenex normal form issues in relation to feasibility and validity of predicate logic formulas.
Syllabus
  • The issue of statement - the name itself, individual constant, individual variable.
  • The syntax, the semantics - denotation, designation, sense, meaning.
  • Basic characteristics of binary arithmetic. The analogy of Boolean algebra and statement logic.
  • Logic connectors as functions defined on }0,1 set.
  • Functional completeness of statement logic, functionally complete systems of statement logic (Sheffer´s and Lukasiewicz´s operator, Pierce “arrow”), functional completeness proof. Application of functional completeness in technical systems.
  • Kinds of axiomatic statement logic, comparison and evidence of axiomatic systems of statement logic equivalency.
  • Disjunctive and conjunctive normal forms, complete disjunctive and conjunctive normal forms and their minimization.
  • Basic issues of 1st grade predicate logic with equivalency.
  • Free and bound variables, opened and closed formulas of predicate logic.
  • Valid and feasible formulas of predicate logic.
  • Kinds of axiomatic predicate logic (axioms and axiom schemes).
  • Issues of decision making possibilities in predicate logic areas where 1st grade predicate logic is applicable.
  • Prenex normal forms, Skolem normal forms, “reduction theorem”.
Literature
    required literature
  • Švejdar, V.: Logika – neúplnost, složitost a nutnost. Academia, Praha 2002.
  • Sochor, A.: Klasická matematická logika. Karolinum, Praha 2001.
Teaching methods
„Lectures and seminars in full-time study; tutorials in part-time study; compulsory seminar participation is 75% in full-time study, compulsory tutorial participation is 50% in part-time study.“
Assessment methods
Assessment methods and criteria The course is completed with a credit and verbal exam. Credit: test – 6 examples (two of them from predicate logic), correct solutions of four examples (one of them from predicate logic). Exam: oral, related to faulty procedures of problem solutions in the test. Two verbal questions, one from the statement logic and one from the predicate logic. Correct answers to both questions in given framework are required to pass the exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
General note: Bb1.
Information on the extent and intensity of the course: 6 hodin KS/semestr.
The course is also listed under the following terms Winter 2007, Winter 2008, Summer 2009, Winter 2009, Winter 2010, Winter 2011, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023, Summer 2025.
  • Enrolment Statistics (Winter 2012, recent)
  • Permalink: https://is.vsfs.cz/course/vsfs/winter2012/N_MaL