Infectious logics are systems which have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated (i) as a way to treat different pathological sentences (like the Liar and the Truth-Teller) differently, namely, by allowing some of them to be truth-value gluts and some others to be truthvalue gaps, and (ii) as a way to treat the semantic pathology suffered by at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof-theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems.

The aim of this article is to discuss the extent to which certain substructural logics are related through the phenomenon of duality. Roughly speaking, metainferences are inferences between collections of inferences, and thus substructural logics can be regarded as those logics which have fewer valid metainferences that Classical Logic. In order to investigate duality in substructural logics, we will focus on the case study of the logics ST and TS, the former lacking Cut, the latter Reflexivity. The sense in which these logics, and these metainferences, are dual has yet to be explained in the context of a thorough and detailed exposition of duality for frameworks of this sort. Thus, our intent here is to try to elucidate whether or not this way of talking holds some ground-specially generalizing one notion of duality available in the specialized literature, the so-called notion of negation duality. In doing so, we hope to hint at broader points that might need to be addressed when studying duality in relation to substructural logics.