| Texto completo | |
| Autor(es): |
Coniglio, Marcelo E.
;
Figallo, Martin
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | LOGIC AND LOGICAL PHILOSOPHY; v. 33, n. 2, p. 33-pg., 2024-01-26. |
| Resumo | |
Tetravalent modal logic (TML) was introduced by Font and Rius in 2000. It is an expansion of the Belnap-Dunn four -valued logic FOUR, a logical system that is well-known for the many applications found in several fields. Besides, TML is the logic that preserves degrees of truth with respect to Monteiro's tetravalent modal algebras. Among other things, Font and Rius showed that TML has a strongly adequate sequent system, but unfortunately this system does not enjoy the cut -elimination property. However, in a previous work we presented a sequent system for TML with the cut -elimination property. Besides, in this same work, it was also presented a sound and complete natural deduction system for this logic. In the present article we continue with the study of TML under a proof -theoretic perspective. In the first place, we show that the natural deduction system that we introduced before admits a normalization theorem. In the second place, taking advantage of the contrapositive implication for the tetravalent modal algebras introduced by A. V. Figallo and P. Landini, we define a decidable tableau system adequate to check validity in the logic TML. Finally, we provide a sound and complete tableau system for TML in the original language. These two tableau systems constitute new (proof -theoretic) decision procedures for checking validity in the variety of tetravalent modal algebras. (AU) | |
| Processo FAPESP: | 22/03862-2 - Métodos de Teoria da Prova para LFIs e Outras Lógicas Não-clássicas: Decidibilidade e Aplicações |
| Beneficiário: | Marcelo Esteban Coniglio |
| Modalidade de apoio: | Auxílio à Pesquisa - Pesquisador Visitante - Internacional |
| Processo FAPESP: | 20/16353-3 - Racionalidade, lógica e probabilidade: RatioLog |
| Beneficiário: | Marcelo Esteban Coniglio |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |