Non-classical Logics (K. Bendová)
Syllabus of the course
(Philosophical Faculty, Charles University)
Goal of the Course
Modal Logics
History. Modalities of necessity and possibility. Strict implication.
Modal systems T, S4, S5, B. Axiomatization of modal logics. Kripke's models.
Completeness theorems through maximal consistent sets. Finding counterexamles
(Beth tableaux). Systems between S4 and S5.
Temporal Logics
Modalities G, H, F, P (strong future, strong past, weak future, weak past).
Axiomatization of temporal logic.
Characterization of various orderings.
Dynamic Logic
Modalities, models, simulation of programs.
Logic of Provability
Modality as provability in Peano Arithmetics, Loeb axiom, models.
Completeness theorem with respect to finite trees.
Other Modal Logics
Deontic logic. Binary modalities. Examples through information transfere.
Intuitionistic Logic
History, motivation. Axioms, provability. Kripke's models, Beth's models.
Completeness theorem. Finding counterexamles. Topological models. Heyting
algebras. Relation to modal logic S4.
Many-valued Logics
History, motivation. Lukasiewicz three-valued logic, three-valued
propositional connectives. Kleene three-valued logic. Interpretation of the
third value. Persistence, relation to modal logic S5, relation to
intuitionistic logic. Other many-valued logics. Possible sets of connectives
(Lukasiewicz, Goedel). Axiomatization. Infinitely many valued logics and
their relation to intuitionistic logics.
Fuzzy Logic
History, motivations. Difference between concepts of vagueness and
uncertainty. Fundamental concepts. Fuzzy logic as many-valued logic.
Pavelka's axiomatization, models, provability, entailment. Applications:
fuzzy regulators.
References:
- Lewis Carl J. - Langford C. H.: Symbolic Logic. The Century Comp.,
New York - London 1932.
- Mleziva Miroslav: Neklasicke logiky (Non classical logics). Svoboda,
Praha 1970.
- Cresswell M. J. - Hughes G. E.: An Introduction to Modal Logic. Methuen,
London - New York 1982.
Last modified: 15 May 1996 by IK.