Logic

Робоча програма навчальної дисципліни (Силабус)

Реквізити навчальної дисципліни

Інформація про викладача

Розподіл годин та занять

The main objective of the course ‘Logic’ is an introduction to contemporary epistemic areas of research concerning the problem of natural and machinic reasoning, foundations of model theory, proof theories and the art of formal and informal proof in general, basics of combinatoric logics, automata theory, as well as their practical implementations into artificial intelligence research, general scientific enquiry, up to some meta-theoretical aspects concerning programming (namely, within the scope of a brief introduction into logical programming paradigm and its implementations) and intersectional areas of set theory, formal theories in mathematics and metamathematics and knowledge bases, expert systems and knowledge representations.

Proceeding throughout the course “Logic”, the listeners would gain the such capabilities, skills and task-solving potencies, as:

- formal representations of the algorithms of human reasoning and inferencing;

- determining the validity of arguments and checking the input data for errors and invalidity;

- performing inductive reasoning procedures in scientific research and professional activity;

- learning theory and using several techniques of formal and informal proofs within the formal systems, such as:

- ‘Gentzen-style’ Sequent Calculus;

- ‘Fitch-style’ proofs;

- Tableaux methodology;

- Automatic resolution systems etc.;

- improving operating skills concerning the concepts of models for the formal systems;

- calculating the truth-contingence of propositional functions, simple and compound propositions;

- building truth tables for any Boolean formula;

- building Venn’s diagrams for the argument validity evaluation;

- building and using logical matrices for many-valued logics;

- operating with the elements of First- and Second-Order Predicate Logics and Modal logics;

- apply rules of inference for theoretical (reasoning) and practical tasks;

- decipher symbolic expressions / modeling semantics for the interpretation of Propositional Functions and Compound Propositions;

The basis of the course is, on one hand, partially represented through other optional disciplines of the bachelor’s general educational programs, on the other, is basically connected with formal scientific and meta-theoretical knowledge and – as it put – a proving algorithms. The course is organized and structured in soundness with the paradigm of polytechnical education, having in mind the inclusion of truly useful parts of vast area of logical investigations for this paradigm. The knowledge and practical assignments are intended to serve as one of the access points (of introduction) to such areas of further professional education as Data Science, Fuzzy sets and Automata theory, Expert systems, AI Research, Machinic reasoning, Machine Learning, cognitive sciences areas, Neuron Networks and Consciousness applied studies withing Mind-Modelling Paradigm.

To provide the most efficient ways of interaction, communication and educational process, a wide specter of tools for distance learning is in effect (Zoom conferences, Google Classroom, social media for lectures, supplementary materials, theoretical and practical tasks and evaluations etc.)

Chapter 1. Formal logical systems: syntax, basic notions, key definitions, symbols, connectives, operators and their purposes

Chapter 2. Classic Propositional logic. Soundness, Consistency, Completeness of CPL. Normal form and PL axiomatics.

Chapter 3. Natural deduction and Fitch-style proofs.

Chapter 4. First-Order Predicate logic. Logic and Set Theory. Decidability problem. Analytic tableaux method.

Chapter 5. 3-valued and n-valued logics for Propositional calculus and FOPL. Alternatives to many-valuedness. Fuzzy set theory basics.

Chapter 6. Modal and Epistemic logic (CPL and FOPL). Modal logics from K to S5, their axiomatics and derivations. Sequent calculus (Gentzen-style proofs).

Chapter 7. Theories of Models. Possible world semantics.

Chapter 8. Logics, philosophy of mind and artificial intelligence. Automated Inferring problem. ‘Hard’ Problem of Consciousness. Strong / Weak AI paradigms.

Chapter 9. Formal systems in Technology, Programming, Applied sciences and beyond.

Нормативні результати навчання, контрольні заходи та терміни виконання оголошуються студентам на першому занятті.

Main basic tools for distance learning: Keynote for visual supplementary materials representations for the lectures. Google classroom for practical (written) tasks for individual work; Zoom conferences for seminaries on theoretical questions concerning lectures.

Additional materials and tools for education include: Ipad2019+Apple Pencil for interactive on-the-go demonstrations and heuristic methods of learning implementing; payed apps for MacOS and iPadOS, namely: BoolTool; Truth Tables; Nyaya; CellularAutomata; Turing; Logic 101; Syllogism; Formulario; Logic Calc; GoodNotes; Baker Street; pytableaux 6.0.4; OmniGraffle; ProofTools; Tree Proof Generator; MOLTAP; Isabelle and many other related applications and materials.

Seminars for deepening the theoretical knowledge, obtained throughout the lectures. In addition, the proposed tasks (both individual and classroom-oriented, interactive ones) serve as well as an introduction to the practical use of formal logical apparatus as a part of their future activities, from knowledge representation in programming and applied engineering, to scientific reasoning and inferencing concerning the structure of reasoning based on logical investigations.

The main materials for the course, as well as additional and optional appendixes and applications, examples and case demonstrations, that are needed for successful completion of the course, as well as supplementary normative documentation are provided by attaching to appropriate and corresponsive posts and topics in Google Classroom, along with the screen-recording of the lectures and its visual supplementary in Keynotes. All the references and literature for preparing to seminars and successful writing on exercises, English language literature, as well as some addition from Ukrainian sources as well, plus annotated summaries of the lectures video captures / tableaux etc., are attached either, usually as separate messages (and pinned throughout the period of their proceedings.

Необов’язкові умови допуску до заліку:

1. Активність на практичних заняттях (як відповідь, так і в формі доповнення).

2. Позитивний результат першої атестації та другої атестації.

3. Відвідування лекційних занять.

Таблиця переведення рейтингових балів до оцінок за університетською шкалою [1]

Attending issues (due to COVID-19)

Due to the current study processual conditions, no rigid control for either lectures or seminars is provided, however, the lectures attendance is recommended.

Inclusive education

The course “Logic” is fully available to any of the listeners with specific needs for learning.

Foreign language

Both theoretical (lectures, supplementary documents – annotated summaries, brief vocabulary of key notions, short printed sketch of each lecture, Keynotes-presentation, outputs of additional applications and widgets or any other supporting software and hardware elements) and practical (the description of the tasks – theoretical questions for the discussions, as well as written tasks, exercises, the examples for each exercise and so on; questions for self-estimation of understanding of the lecture materials and any other related content) course compounds are given in English, with appropriate use of textbooks and handbooks of Anglo-American publishing as initial materials when preparing the lectures and other materials of the course content.

Процедура оскарження результатів контрольних заходів

Студенти мають можливість підняти будь-яке питання, яке стосується процедури контрольних заходів та очікувати, що воно буде розглянуто згідно із наперед визначеними процедурами.

Студенти мають право оскаржити результати контрольних заходів, але обов’язково аргументовано, пояснивши з яким критерієм не погоджуються відповідно до оціночного листа та/або зауважень.

Календарний рубіжний контроль

Проміжна атестація студентів (далі – атестація) є календарним рубіжним контролем. Метою проведення атестації є підвищення якості навчання студентів та моніторинг виконання графіка освітнього процесу студентами [2].

Академічна доброчесність

Політика та принципи академічної доброчесності визначені у розділі 3 Кодексу честі Національного технічного університету України «Київський політехнічний інститут імені Ігоря Сікорського». Детальніше: https://kpi.ua/code.

Норми етичної поведінки

Норми етичної поведінки студентів і працівників визначені у розділі 2 Кодексу честі Національного технічного університету України «Київський політехнічний інститут імені Ігоря Сікорського». Детальніше: https://kpi.ua/code.

[1] Оцінювання результатів навчання здійснюється за рейтинговою системою оцінювання відповідно до рекомендацій Методичної ради КПІ ім. Ігоря Сікорського , ухвалених протоколом №7 від 29.03.2018 року.

[2] Рейтингові системи оцінювання результатів навчання: Рекомендації до розроблення і застосування. Київ: КПІ ім. Ігоря Сікорського, 2018. 20 с.