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

Many-Valued and Applied Modal Logics 2003/4

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

Syllabus

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 sets (fuzzy control).

Summer term

  1. Applied modal logics: Epistemic and doxastic modal logic (axioms, semantics). Deontic modal logic (axioms, semantics).
  2. 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.

Literature

Required

Recommended

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: Applied modal and polymodal logics (5 lectures, this webpage)

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