In 1986, I. Mikenberg, N. da Costa and R. Chuaqui introduced the semantic notion of quasi-truth defined by means of partial structures. In such structures, the predicates are seen as triples of pairwise disjoint sets: the set of tuples which satisfies, does not satisfy and can satisfy or not the predicate, respectively. The syntactical counterpart of the logic of partial truth is a rather complicated first-order modal logic. In the present paper, the notion of predicates-as-triples is recursively extended, in a natural way, to any complex formula of the first-order object language. From this, a new definition of quasi-truth is obtained. The proof-theoretic counterpart of the new semantics is a first-order paraconsistent logic whose propositional base is a 3-valued logic belonging to hierarchy of paraconsistent logics known as Logics of Formal Inconsistency, which was proposed by W. Carnielli and J. Marcos in 2001.
A quase-verdade ou verdade pragmática foi introduzida por Newton da Costa e seus colaboradores como uma estrutura formal que pode ser empregada como a concepção de verdade inerente às ciências empíricas. No presente artigo, iremos abordar o conceito de quaseverdade por meio de duas noções (formalizações) distintas, a saber, a definição de quasesatisfação, proposta por Bueno e de Souza (1996), e a noção de satisfação pragmática, introduzida por Coniglio e Silvestrini (2014). A despeito da definição de Bueno e de Souza permitir uma interpretação da quase-verdade mais próxima de uma visão empirista, mostramos o quanto ela pode ser discrepante do ponto de vista formal com a proposta original de da Costa. Desse modo, defendemos o uso da formalização da quase-verdade por meio da noção de satisfação pragmática, uma definição mais geral, visto que ela engendra lógicas paraconsistentes adequadas para tal noção.
Newton da Costa and his collaborators have introduced the notion of quasi-truth by means of partial structures, and for this purpose, they conceived the predicates as ordered triples: the set of tuples which satisfies, does not satisfy and can satisfy or not the predicate, respectively (the latter represents lack of information). This approach provides a conceptual framework to analyse the use of (first-order) structures in science in contexts of informational incompleteness. In this Thesis, the notion of predicates as triples is extended recursively to any complex formula of the first-order object language. From this, a new definition of quasi-truth via the notion of pragmatic satisfaction is obtained. We obtain the proof-theoretic counterpart of the logic underlying our new definition of quasi-truth, namely, the three-valued paraconsistent logic LPT1, which is presented axiomatically in a first-order language. We relate the notion of quasi-truth with some existing paraconsistent logics. We defend that the formalization of (open) society semantics when combined with the modulated quantifiers constitutes an alternative to capture the inductive component present in scientific activity, and show, from this, that the original proposal of da Costa and collaborators can be explained in terms of the new concept of modulated societies.
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