460-4034/02 – Advanced Logic (VPL)
Gurantor department | Department of Computer Science | Credits | 4 |
Subject guarantor | prof. RNDr. Marie Duží, CSc. | Subject version guarantor | prof. RNDr. Marie Duží, CSc. |
Study level | undergraduate or graduate | Requirement | Optional |
Year | 2 | Semester | summer |
| | Study language | Czech |
Year of introduction | 2015/2016 | Year of cancellation | 2022/2023 |
Intended for the faculties | FEI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
The goal of the course is providing knowledge on particular methods of reasoning and automatic theorem proving. We focus on the development of these methods in the area of relational and algebraic theories and philosophy of mathematics. The course also aims at using the proof methods in theoretical computer science.
Teaching methods
Lectures
Seminars
Individual consultations
Tutorials
Summary
The goal of the course is providing knowledge on particular methods of reasoning and automatic theorem proving. We focus on the development of these methods in the area of relational and algebraic theories and philosophy of mathematics. The course also aims at using the proof methods in theoretical computer science.
Compulsory literature:
E. Mendelson. Introduction to Mathematical Logic. Chapman & Hall/CRC, 2001.
P. Hájek: Metamathematics of Fuzzy Logic. Kluwer, 1998.
Recommended literature:
P. Hájek: Metamathematics of Fuzzy Logic. Kluwer, 1998.
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
There are not defined other requirements for student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
1) Proof calculi, consistence and completeness.
2) Hilbert-style proof calculus.
3) Logical theories; completeness and incompleteness of a theory, decidability.
4) Theory of relations; equivalence and orderings.
5) Algebraic theories; groups, rings and fields.
6) Lattice theory, conceptual lattices.
7) Theories of arithmetic, Gödel results; incompleteness theorems.
8) Theory of recursive functions and algorithms.
9) Sequent calculi
10) Intensional logics and Kripke semantics.
Seminars:
1) Proof calculi, consistence and completeness.
2) Hilbert-style proof calculus.
3) Logical theories; completeness and incompleteness of a theory, decidability.
4) Theory of relations; equivalence and orderings.
5) Algebraic theories; groups, rings and fields.
6) Lattice theory, conceptual lattices.
7) Theories of arithmetic, Gödel results; incompleteness theorems.
8) Theory of recursive functions and algorithms.
9) Sequent calculi
10) Intensional logics and Kripke semantics.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction