A classical Gentzen-type system is one which employs two-sided sequents, together with structural and logical rules of a certain characteristic form. A decent Gentzen-type system should allow for direct proofs, which means that it should admit some useful forms of cut elimination and the subformula property. In this tutorial we explain the main difficulty in developing classical Gentzen-type systems with these properties for many-valued logics. We then illustrate with numerous examples the various possible ways of overcoming this difficulty. Our examples include practically all 3-valued logics, the most important class of 4-valued logics, as well as central infinite-valued logics (like Gödel-Dummett logic, S5 and some substructural logics).
|Number of pages||10|
|Journal||Proceedings of The International Symposium on Multiple-Valued Logic|
|State||Published - 2001|
|Event||31st IEEE International Symposium on Multiple-Valued Logic (ISMVL 2001) - Warsaw, Poland|
Duration: 22 May 2001 → 24 May 2001