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Infectious logics are systems which have a truthvalue that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies fourvalued 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 TruthTeller) differently, namely, by allowing some of them to be truthvalue gluts and some others to be truthvalue gaps, and (ii) as a way to (...) 

The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic \. We prove that the description of the algebraic counterpart of the left variable inclusion companion of a given logic \ is related to the construction of Płonka sums of the matrix models of \. This observation allows to obtain a Hilbertstyle axiomatization of the logics of left variable inclusion, to describe the structure of their reduced models, and to locate (...) 

This paper presents a semantical analysis of the Weak Kleene Logics Kw3 and PWK from the tradition of Bochvar and Halldén. These are threevalued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical con sequence in PWK – that is, we individuate necessary and sufficient conditions for a set. 



In this paper, we consider some contributions to the model theory of the logic of formal inconsistency $\mathsf{QmbC}$ as a reply to Walter Carnielli, Marcelo Coniglio, Rodrigo Podiacki and Tarcísio Rodrigues’ call for a ‘wider model theory.’ This call demands that we align the practices and techniques of model theory for logics of formal inconsistency as closely as possible with those employed in classical model theory. The key result is a proof that the Keisler–Shelah isomorphism theorem holds for $\mathsf{QmbC}$, i.e. (...) 

In the literature, Weak Kleene logics are usually taken as threevalued logics. However, Suszko has challenged the main idea of manyvalued logic claiming that every logic can be presented in a twovalued fashion. In this paper, we provide twovalued semantics for the Weak Kleene logics and for a number of fourvalued subsystems of them. We do the same for the socalled Logics of Nonsense, which are extensions of the Weak Kleene logics with unary operators that allow looking at them as (...) 

We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone duality from one side and the representation of involutive bisemilattices as Płonka sum of Boolean algebras, from the other. Furthermore, we show that the dual space of an involutive bisemilattice can be viewed as a GR space with involution, a generalization of the spaces introduced by Gierz and Romanowska equipped with an involution as additional operation. 

Płonka sums consist of an algebraic construction similar, in some sense, to direct limits, which allows to represent classes of algebras defined by means of regular identities. Recently, Płonka sums have been connected to logic, as they provide algebraic semantics to logics obtained by imposing a syntactic filter to given logics. In this paper, I present a very general topological duality for classes of algebras admitting a Płonka sum representation in terms of dualisable algebras. 

Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of manyvalued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic threevalued connectives of LP language) by the addition of unary and binary connectives. Tamminga has also applied this technique to the paracomplete (...) 