Australasian Journal of Logic 18 (1):29-52 (2021)

Bruno Da Re
Universidad de Buenos Aires (UBA)
Damian Szmuc
Universidad de Buenos Aires (UBA)
This article is concerned with an exploration of a family of systems—called immune logics—that arise from certain dualizations of the well-known family of infectious logics. The distinctive feature of the semantic of infectious logics is the presence of a certain “infectious” semantic value, by which two different though equivalent things are meant. On the one hand, it is meant that these values are zero elements for all the operations in the underlying algebraic structure. On the other hand, it is meant that these values behave in a value-in-value-out fashion for all the operations in the underlying algebraic structure. Thus, in a rather informal manner, we will refer to immune logics as those systems whose underlying semantics count with a certain “immune” semantic value behaving in a way that is somewhat dual to that of the infectious values. In a more formal manner, carrying out this dualization will prove to be not as straightforward as one could imagine, since the two characterizations of infectiousness discussed above lead to two different outcomes when one tries to conduct them. We explore these alternatives and provide technical results regarding them, and the various logical systems defined using such semantics.
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DOI 10.26686/ajl.v18i1.6582
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References found in this work BETA

Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
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Citations of this work BETA

Secrecy, Content, and Quantification.Thomas Macaulay Ferguson - 2021 - Análisis Filosófico 41 (2):285-302.
A Reinterpretation of Beall’s ‘Off-Topic’ Semantics.Jeremiah Joven B. Joaquin - forthcoming - Journal of Logic, Language and Information:1-13.
Infectious and Transparent Emotivism.Jeremiah Joven Joaquin - 2021 - Journal of Applied Non-Classical Logics 32 (1):1-10.
Many-Valued Logics and Bivalent Modalities.Edson Bezerra & Giorgio Venturi - forthcoming - Logic and Logical Philosophy:1-26.

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