Applied logic 1000-1M09LST
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.
Type of course
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
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