Many-Valued Logics and Interpreted 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 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.

Literature

Required

• Handouts for lectures #1, #2 (RTF, Czech).
• Kijania-Placek, K.: What Difference Does it Make: Three Truth-Values or Two Plus Gaps? Erkenntnis 56 (2002), 83-98.
• Hajek, P., Godo, L.: Deductive Systems of Fuzzy Logic. Tatra Mountains Math. Publ. 13 (1997), 35-66. Parts 1-2.
• Novak, V., Cerny, M., Nekola, J.: Fuzzy mnoziny - perspektivy, problemy a aplikace (Czech, "Fuzzy sets - perspectives, problems and applications"). Pokroky MFA 29 (1984), 6, 126-137. Parts 1-2.2.
• Stanford Encyclopedia of Philosophy, entries Many-Valued Logic, Fuzzy Logic, Modal Logic, Temporal Logic.

Recommended

• The rest of Hajek-Godo and Novak-Cerny-Nekola cited above.
• Gabbay, D., Guenthner, F. (Eds.): Handbook of Philosophical Logic. (Relevant chapters.)
• Hajek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht, 1998. (The parts corresponding to Hajek-Godo cited above.)
• Stanford Encyclopedia of Philosophy, entries Paraconsistent Logic, Inconsistent Mathematics, Dialetheism, Substructural Logics.
• Duc, H.N.: Resource-Bounded Reasoning about Knowledge. PhD thesis, Universität Leipzig, 2001.
• Duc, H.N.: Semantical Investigations in the Logic of Actions and Norms. Master thesis, Institut für Logik und Wissenschaftstheorie, 1995.

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)