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Type: Artigo
Title: On the way to a wider model theory: completeness theorems for first-order logics of formal inconsistency
Author: Rodrigues, T.
Podiacki, R.
Coniglio, M.E.
Carnielli, W..
Abstract: This paper investigates the question of characterizing first-orderLFIs (logics of formal inconsistency) by means of two-valued semantics.LFIs are powerfulparaconsistent logics that encode classical logic and permit a finer distinction be-tween contradictions and inconsistencies, with a deep involvement in philosophicaland foundational questions. Although focused on just one particular case, namely,the quantified logicQmbC, the method proposed here is completely general forthis kind of logics, and can be easily extended to a large family of quantifiedparaconsistent logics, supplying a sound and complete semantical interpretationfor such logics. However, certain subtleties involving term substitution and re-placement, that are hidden in classical structures, have to be taken into accountwhen one ventures into the realm of non-classical reasoning. This paper showshow such difficulties can be overcome, and offers detailed proofs showing that asmooth treatement of semantical characterization can be given to all such logics.Although the paper is well-endowed in technical details and results, it has a sig-nificant philosophical aside: it shows how slight extensions of classical methodscan be used to construct the basic model theory of logics that are weaker than tra-ditional logic due to the absence of certain rules present in classical logic. Severalsuch logics, however, as in the case of theLFIs treated here, are notorious fortheir wealth of models precisely because they do not make indiscriminate use ofcertain rules; these models thus require new methods. In the case of this paper, byjust appealing to a refined version of the Principle of Explosion, or Pseudo-Scotus,some new constructions and crafty solutions to certain non-obvious subtleties areproposed. The result is that a richer extension of model theory can be inaugurated,with interest not only for paraconsistency, but hopefully to other enlargements oftraditional logic.
Subject: Logica paraconsistente
Country: Inglaterra
Editor: Cambridge University Press
Citation: Review Of Symbolic Logic. Cambridge University Press, v. 7, n. 3, p. 548 - 578, 2014.
Rights: fechado
Identifier DOI: 10.1017/S1755020314000148
Date Issue: 2014
Appears in Collections:IFCH - Artigos e Outros Documentos

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