Applied logic

General data

Course ID:	1000-1M09LST
Erasmus code / ISCED:	11.1 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Applied logic
Name in Polish:	Logika stosowana
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective monographs
Short description:	The lecture presents selected paradigms and methods of formal logic accompanied by descriptions of the fields of their application. The topics of lecture are mostly related to relatively simple, yet practically implementable logical models.
Full description:	Language and methodology of formal logic. Proper construction of formulae. Formal system, axioms, syntax and semantics. Soundness and completeness of propositional logic. Compactness and deduction principle. Decidability and computational complexity of satisfiability problems. Applications of ropositional logic in games, circuit verification, test theory, etc. Standard modal logic systems. Axioms and formulae determining properties of modal logics. Inference methods. Kripke models and semantics in modal logics. Various definitions of semantic consequence. Soundness and completeness for standard modal logic w.r.t. model with valuation. Satisfiability for Kripke models. Decidability and computational complexity of satisfiability problems for modal logic S5. Application of modal logics to knowledge representation, program verification, multi-party games, etc. Fuzzy sets and systems, membership functions, fuzzy set operators, T-norms and S-norms. Complement of fuzzy set. Inference in fuzzy systems, linguistic rules, various versions of implication. Clauses, resolution principle and proofs based on resolution. Resolution-based propositional fuzzy logic (possibilistic logic). Soundness and completeness of possibilistic logic. Truth-functional fuzzy logic. Models utilising fuzzy membership. Soundness and completeness of truth-functional fuzzy logic. Application of fuzzy sets and fuzzy logic in control systems, decision support and expert systems, knowledge engineering, etc.
Bibliography:	S.Popkorn, First steps in modal logic. Cambridge University Press, Cambridge 1994 G.E. Hughes, M.J. Cresswell, A companion to modal logic. Rutlege, Kegan and Paul Publishers, 1985 R. Kruse, J. Gebhardt, F. Klawonn, Foundations of Fuzzy Systems. John Wiley and Sons, 1994

This course is not currently offered.

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