A sequent calculus for the three-valued and intuitionistic logic I1
Introduction to Mathematical logic: an Algebraic and Topological approach
| Full text | |
| Author(s): |
Coniglio, Marcelo Esteban
[1, 2]
;
Figallo-Orellano, Aldo
[2, 3]
;
Hernandez-Tello, Alejandro
[4]
;
Perez-Gaspar, Miguel
[5]
Total Authors: 4
|
| Affiliation: | [1] Univ Estadual Campinas, UNICAMP, Inst Philosophy & Humanities IFCH, Campinas, SP - Brazil
[2] Univ Estadual Campinas, Ctr Log Epistemol & Hist Sci CLE, UNICAMP, Campinas, SP - Brazil
[3] Univ Nacl Sur UNS, Dept Matemat, Buenos Aires, DF - Argentina
[4] Univ Tecnol Mixteca UTM, Inst Fis & Matemat, Oaxaca, Oaxaca - Mexico
[5] Univ Nacl Autonoma Mexico, Fac Ingn, Mexico City, DF - Mexico
Total Affiliations: 5
|
| Document type: | Journal article |
| Source: | JOURNAL OF APPLIED LOGICS-IFCOLOG JOURNAL OF LOGICS AND THEIR APPLICATIONS; v. 9, n. 1, p. 175-197, JAN 2022. |
| Web of Science Citations: | 0 |
| Abstract | |
In 2001, W. Carnielli and Marcos considered a 3-valued logic in order to prove that the schema phi V (phi -> psi) is not a theorem of da Costa's logic C-omega. In 2006, this logic was studied (and baptized) as G(3)' by Osorio et al. as a tool to define semantics of logic programming. It is known that the truth-tables of G(3)' have the same expressive power than the one of Lukasiewicz 3-valued logic as well as the one of Godel 3-valued logic G(3). From this, the three logics coincide up-to language, taking into acccount that 1 is the only designated truth-value in these logics. From the algebraic point of view, Canals-Frau and Figallo have studied the 3-valued modal implicative semilattices, where the modal operator is the wellknown Moisil-Monteiro-Baaz A operator, and the supremum is definable from this. We prove that the subvariety obtained from this by adding a bottom element Delta is term-equivalent to the variety generated by the 3-valued algebra of G(3)' . The algebras of that variety are called G(3)'-algebras. From this result, we obtain the equations which axiomatize the variety of G(3)'-algebras. Moreover, we prove that this variety is semisimple, and the 3-element and the 2-element chains are the unique simple algebras of the variety. Finally an extension of G(3)' to first-order languages is presented, with an algebraic semantics based on complete G(3)'-algebras. The corresponding soundness and completeness theorems are obtained. (AU) | |
| FAPESP's process: | 16/21928-0 - Non-deterministic semantics for logics of formal inconsistency |
| Grantee: | Aldo Figallo Orellano |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |