We argue that many-valued logics (MVLs) can be useful in analysing informational conflicts by using society semantics (SSs). This work concentrates on four-valued Łukasiewicz logic. SSs were proposed by Carnielli and Lima-Marques (1999, Advances in Contemporary Logic and Computer Science, 235, 33–52) to deal with conflicts of information involving rational agents that make judgements about propositions according to a given logic within a society, where a society is understood as a collection $\mathcal{A}$ of agents. The interesting point of such semantics is that a new logic can be obtained by combining the logic of the agents under some appropriate rules. Carnielli and Lima-Marques (1999, Advances in Contemporary Logic and Computer Science, 235, 33–52) defined SSs for the three-valued logics $I^{1}$ and $P^{1}$. In this kind of semantics, all the agents reason according to classical logic (CL) and the molecular formulas behave in the same way as in CL (the non-classical character of these logics only appears at the propositional level). Marcos (unpublished data) provided SSs with classical agents for the three-valued Łukasiewicz logic Ł$_{3}$, but in this case, the molecular formulas do not behave classically. We prove here that one can characterize Ł$_{4}^{\prime}$, a conservative extension of Ł$_{4}$ obtained by adding a connective $\blacktriangledown$, by means of a closed society where the agents reason according to Ł$_{3}$. We shall emphasize the importance of recovery operators in the construction of this class of societies. Moreover, we shall relate this semantics to Suszko’s view on the ‘two-valuedness’ of logic.

A Tese de Suszko (SUSZKO, 1977) afirma a existência de somente dois valores lógicos, o verdadeiro lógico, o verdadeiro e o falso. Neste artigo, argumento em favor da compatibilidade da Tese de Suszko com a tese do Pluralismo Lógico tal como formulado por Hjortland (HJORTLAND, 2011).

In this paper, we investigate the family LS0.5 of many-valued modal logics LS0.5's. We prove that the modalities of necessity and possibility of the logics LS0.5's capture well-defined bivalent concepts of logical validity and logical consistency. We also show that these modalities can be used as recovery operators.

In this paper we study a new operator of strong modality ⊞, related to the non-contingency operator ∆. We then provide soundness and completeness theorems for the minimal logic of the ⊞-operator.