Colegas: Apraz-nos (!) informar que nosso artigo abaixo acaba de ser publicado pelo The Review of Symbolic Logic:
"Logics of Formal Inconsistency Enriched with Replacement: An Algebraic and Modal Account " (Walter Carnielli, Marcelo E. Coniglio and David Fuenmayor) The Review of Symbolic Logic https://www.doi.org/10.1017/S1755020321000277. Published online by Cambridge University Press: 02 July 2021 https://www.cambridge.org/core/journals/review-of-symbolic-logic/article/abs/logics-of-formal-inconsistency-enriched-with-replacement-an-algebraic-and-modal-account/02C1B4CF921AA2998427A258CA35127F =========================================== Abstract It is customary to expect from a logical system that it can be algebraizable, in the sense that an algebraic companion of the deductive machinery can always be found. Since the inception of da Costa’s paraconsistent calculi, algebraic equivalents for such systems have been sought. It is known, however, that these systems are not self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok–Pigozzi. The same negative results hold for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, several systems belonging to this class of logics are only characterizable by semantics of a non-deterministic nature. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by extending with rules several LFIs weaker than C_1 , thus obtaining the replacement property (that is, such LFIs turn out to be self-extensional). Moreover, these logics become algebraizable in the standard Lindenbaum–Tarski’s sense by a suitable variety of Boolean algebras extended with additional operations. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied. In addition, a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E \circplus E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. the proposed algebraic semantics. ====== As primeiras 10 pessoas que tiverem interesse poderão receber uma cópia oficial (distribuída pelo RSL) Abraços, Walter (em nome de Marcelo e David) ======================== Walter Carnielli CLE and Department of Philosophy University of Campinas –UNICAMP, Brazil https://waltercarnielli.com/ -- LOGICA-L Lista acadêmica brasileira dos profissionais e estudantes da área de Lógica <logica-l@dimap.ufrn.br> --- Você está recebendo esta mensagem porque se inscreveu no grupo "LOGICA-L" dos Grupos do Google. Para cancelar inscrição nesse grupo e parar de receber e-mails dele, envie um e-mail para logica-l+unsubscr...@dimap.ufrn.br. Para ver esta discussão na web, acesse https://groups.google.com/a/dimap.ufrn.br/d/msgid/logica-l/CAOrCsLdN%3DArurCV8C0qKXp58mj0-3JtDWSKpcfaaehr%2B5o5TDQ%40mail.gmail.com.
