Non-transitive counterparts of every Tarskian logic

Building on the work done by Cobreros, Egre, Ripley, and van Rooij on a non-transitive version of CL denoted by them as ST, we present a generalization of this phenomenon, consisting of providing technical means to find a non-transitive analog for every Tarskian logic. We do this by building on Wojcicki's and Frankowski's results on the characterization of Tarskian logics and p-logics in terms of classes of matrices and p-matrices, respectively. The key to our result is the extension of certain algebras and matrices with so-called infectious values.