PHV445 Formal Logic, Knowledge Representation and Reasoning

Faculty of Arts
Spring 2026
Extent and Intensity
2/0/0. 5 credit(s). Type of Completion: k (colloquium).
Teacher(s)
prof. PhDr. BcA. Jiří Raclavský, Ph.D. (lecturer)
Guaranteed by
prof. PhDr. BcA. Jiří Raclavský, Ph.D.
Department of Philosophy – Faculty of Arts
Supplier department: Department of Philosophy – Faculty of Arts
Prerequisites
Introductory course to logic (e.g. propositional logic connectives, ...), e.g. PHBL2 Formální logika, recommended.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 11 fields of study the course is directly associated with, display
Course objectives
  • (1) Acquiring the essential notions of FORMAL LOGIC, in particular, (classical) quantified (1st-order, predicate) logic, see Course Contents for details.
  • (2) Most of the course is an application of (selected parts of) MATHEMATICAL LOGIC on natural language, i.e. on everyday rational reasoning. In computer science, esp. AI, it form an important part of KNOWLEDGE INTERPRETATION AND REASONING.
  • (3) Some lectures focus on theory (e.g. syntax/semantics of quantified logic, paradoxes), and some lectures focus on solutions to practical problems (e.g. equivalences/negations of propositions/formulas, arguments checking, natural deduction).
  • (4) The course provides minimal fundaments for the following parts of philosophy: non-classical/philosophical logic, philosophy of language/computing/AI/logic/mathematics etc., formal epistemology, formal ontology, formal ethics.
  • (5) Also, the course provides a specific theoretic background for computer linguistics. (Parts of most of the course are taught within computer science and mathematics.)
    • Learning outcomes
  • (1) Acquiring the essential notions of formal logic, in particular, (classical) quantified logic, see Course Contents for details.
  • (2) Increasing logical reasoning and critical thinking.
  • (3) Acquiring skills in the representation of knowledge (natural language processing) and reasoning in the sense of AI, computer science, formal semantics, analytic philosophy etc.
  • (4) Exercising analytical and algorithmic thinking, both on natural and formal examples.
  • (5) Acquiring some deeper knowledge about logic as a science and its application.
    • Syllabus
    • The course in mostly an introduction to (1st-order) quantified logic (FOL):
    • (1) Informal introduction, Predication, quantification.
    • (2) Formal language.
    • (3) Selected logical truths. Square of opposition (negations, equivalences).
    • (4) Syllogistics. Validity checking using Venn diagrams.
    • (5) FOL with identity and descriptions.
    • (6) Logical consequence. Interpretation of formulas.
    • (7) Axiomatisation of formalized theories. Their properties, in/completeness theorems.
    • (8) Higher-order logics, logics of classes/relations.
    • (9) Natural deduction for FOL.
    • (10) Arguments checking by semantic counter-examples.
    • (11) Logic and computers.
    • (12) Semantic tableaux for FOL.
    Literature
      recommended literature
    • RACLAVSKÝ, Jiří. Úvod do logiky: klasická predikátová logika ([Introduction to Logic: Classical Predicate Logic). 1. vyd. Brno: Masarykova univerzita, 2015, 348 pp. ISBN 978-80-210-7867-3. URL info
    • RACLAVSKÝ, Jiří. Úvod do logiky: klasická výroková logika ([Introduction to Logic: Classical Propositional Logic). 1. vyd. Brno: Masarykova univerzita, 2015, 238 pp. ISBN 978-80-210-7790-4. URL info
      not specified
    • RUSSELL, Stuart J. and Peter NORVIG. Artificial intelligence : a modern approach. Edited by Ming-Wei Chang - Jacob Devlin - Anca Dragan - David Forsyth - Ian Good. Fourth edition, global editi. Harlow: Pearson, 2022, 1166 stran. ISBN 9781292401133. info
    • GORANKO, Valentin. Logic as a tool : a guide to formal logical reasoning. First published. Chichester: Wiley, 2016, xxii, 358. ISBN 9781118880005. info
    • RAUTENBERG, Wolfgang. A concise introduction to mathematical logic. Third edition. New York: Springer, 2010, xxi, 319. ISBN 9781441912206. info
    • LEARY, Christopher C. A friendly introduction to mathematical logic. New Jersey: Prentice-Hall, 2000, xiv, 218. ISBN 0130107050. info
    Teaching methods
    Classes containing exercises. E-learning with regular e-homeworks. Numerous study materials: PDF presentations, texts, e-homeworks, and quizzes.
    Assessment methods
  • (1) REGULAR HOMEWORKS = condition required before the exam. During the semester, at least 80 % of regular e-tests (every week 1-2) must be completed (each e-test must receive at least 80 % of points).
  • (2) FINAL EXAM. An e-test via computer. The questions are similar to those from homeworks. (For few, the exam is not required; they successfully pass if filling the homeworks.) For A mark approx. 80 % of questions must be correctly answered.
  • (3) BONUS (non-obligatory surplus activity): increasing received e-test mark by 1 degree (e.g. from D to C) for each of (a)-(c) (cumulative increasing is possible). (a) Attendance to classes, (b) activities in classes (answering topic-related questions), (c) answering questions on selected texts (by analytic philosophers) studied at home. For minimum points, see the Czech version above. Points from activities are recorded in IS during the semester.
    • Náhradní absolvování
    Combined students (students on foreign stay, long-termed ill, ...): contact the teacher for details and agreement, self-study of materials from Interactive syllabi, and filling regular homeworks. Attendance to classes brings surplus points, but the minimum required points can be gathered without attendance from homeworks.
    Language of instruction
    Czech
    Follow-Up Courses
    Study support
    https://is.muni.cz/auth/el/phil/jaro2026/PHV445/index.qwarp
    Further Comments
    Study Materials
    The course is taught once in two years.
    The course is taught every week.
    Teacher's information
    http://www.phil.muni.cz/~raclavsky/logika/
    The course is also listed under the following terms Spring 2025.
    • Enrolment Statistics (Spring 2026, recent)
    • Permalink: https://is.muni.cz/course/phil/spring2026/PHV445