Algebraic Valuations as Behavioral Logical Matrices

The newly developed behavioral approach to the algebraization of logics extends the applicability of the methods of algebraic logic to a wider range of logical systems, namely encompassing many-sorted languages and non-truth-functionality. However, where a logician adopting the traditional approach to algebraic logic finds in the notion of a logical matrix the most natural semantic companion, a correspondingly suitable tool is still lacking in the behavioral setting. Herein, we analyze this question and set the ground towards adopting an algebraic formulation of valuation semantics as the natural generalization of logical matrices to the behavioral setting, by establishing a few simple but promising results. For illustration, we will use da Costa’s paraconsistent logic C1.