Many-valued semantics, besides providing a natural semantical interpretation for several non-classical logics, constitute a very sharp tool for investigating and understanding meta-logical properties in general. Although open to debates from the philosophical perspective, seen from the mathematical viewpoint many-valued matrices and algebras are perfectely well-defined mathematical objects with several attractive properties. This tutorial intends to review the main results, techniques and methods concerning the application of the many-valued approach to logic as a whole.

Description of the contents of the tutorial:

• A bit of history: P. Bernays, A. Tarski, J. Lukasiewicz, S. Jaskowski, S. Kleene, K. Gödel, J. Dugundji, N. da Costa, M. Sette.
• Finite-valued matrices and semantics
• Applications to the foundations of mathematics
• Independence and non-admissibility of axioms and rules
• Non-characterizability of modal, intuitionistic and paraconsistent logics via finite-valued semantics
• A bit of proof theory
• Many-valuedness and databases
• Translations between many-valued semantics and applications
• Dyadic semantics versus many-valued semantics
• The society semantics and the possible-tanslations semantics with many-valued bases
• Interpretations of quantum mechanics

References

C. Caleiro, W. Carnielli, M. E. Coniglio and J. Marcos. Dyadic semantics for many-valued logics. Manuscript, availabe at CLC-IST, Lisbon

W. A. Carnielli. Systematization of the finite manyvalued logics through the method of tableaux. The Journal of Symbolic Logic 52 (1987), nº2, 473-493.

W. A. Carnielli ; J. Marcos and S. de Amo. Formal inconsistency and evolutionary databases. Logic and Logical Philosophy vol.8 (2000), 115-152

R. Hähnle, Advanced many-valued logics. Handbook of Philosophical Logic, Vol. 2, 297--395, Kluwer Acad. Publ., Dordrecht, 2001.

S. Gottwald, A Treatise on Many-Valued Logics. Studies in Logic and Computation, vol. 9, Research Studies Press Ltd., Baldock.

Lecture Notes