Libor Behounek - Logic - Teaching - Many-Valued Logics and Interpreted Modal Logics

Many-Valued Logics and Interpreted Modal Logics 2003/4

Two blocks of lectures within Marta Bilkova's course Non-Classical Logics in 2003/4.


Winter term

  1. Many-valued logics: Matrices, designated values, tautologies, defined connectives. 3-valued logics of Bochvar, Kleene, McCarthy, Lukasiewicz, and Gödel. The laws of Excluded Middle and Non-Contradiction, the Principle of Bivalence, truth-functionality.
  2. Fuzzy logic: Fuzziness vs. probability, possibility etc. Fuzzy logic in the broad and narrow sense. Continuous t-norms (esp. Gödel, Lukasiewicz, product) and their residua. Mostert-Shields characterization theorem (proof omitted). Hajek's Basic Logic and its extensions G, L, and Pi - axioms, semantics. Completeness theorems (proofs omitted), the (local) deduction theorem. Fuzzy predicate calculi. Applied fuzzy methods (fuzzy control).

Summer term

  1. Interpreted modal logics: Epistemic and doxastic modal logic (axioms, semantics). Deontic modal logic (axioms, semantics).
  2. Interpreted polymodal logics: Temporal logic (axioms, semantics). Fusion of unimodal logics (axioms, semantics). Multi-agent epistemic modal logic, common knowledge (axioms, semantics). Dynamic logic (axioms, semantics). Limitations of the applicability of modal logics, an outline of dynamic improvements (dynamic deontic logic, dynamic epistemic logic).
  3. An overview of non-classical logics.




Non-Classical Logics in 2003/4

Marta Bilkova's course Non-Classical Logics had the following structure in 2003/4:

Winter term

  1. Marta Bilkova: Modal logic (8 lectures)
  2. Libor Behounek: Many-valued and fuzzy logics (3 lectures, this webpage)

Summer term

  1. Marta Bilkova: Modal logic (2 lectures)
  2. Michal Pelis: Intuitionistic logic and inferential erotetic logic (6 lectures)
  3. Libor Behounek: Interpreted modal logics (5 lectures, this webpage)

Last update of this page: Sunday, 11-Apr-2021 22:47:32 CEST