Abstract

Society Semantics, introduced by W. Carnielli and M. Lima-Marques, is a method for obtaining new logics from the combination of agents of a given logic. The goal of this paper is to present several generalizations of this method, as well as to show some applications to many-valued logics. After a reformulation of Society Semantics in a wider setting, we develop in detail two examples of application of the new formalism, characterizing a hierarchy of paraconsistent logics called Pn and a hierarchy of paracomplete logics In. We also propose three further generalizations, obtaining Society Semantics for several many-valued logics, including a hierarchy of logics called In Pk which are both paraconsistent and paracomplete.