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Room P3.10, Mathematics Building
Combining valuations with society semantics
Society Semantics, introduced by W. Carnielli and M. Lima-Marques, is a method for obtaining new logics from the combination of agents (valuations) of a given logic. The goal of this talk 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 two examples of application of the new formalism, characterizing a hierarchy of paraconsistent logics called $P^n$ (for every natural number $n$) and a hierarchy of paracomplete logics $I^n$ (for every natural number $n$). We also propose three increasing generalizations, obtaining Society Semantics for several many-valued logics, including a hierarchy of logics called $I^nP^k$ which are both paraconsistent and paracomplete.