Conjunction and Disjunction in Infectious Logics

In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). Berlin: Springer. pp. 268-283 (2017)
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Abstract
In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them discusses our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction.
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Archival date: 2018-04-13
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References found in this work BETA
Logics of Nonsense and Parry Systems.Ferguson, Thomas Macaulay

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Semantical Analysis of Weak Kleene Logics.Ciuni, Roberto & Carrara, Massimiliano
Theories of Truth Based on Four-Valued Infectious Logics.Szmuc, Damian; Da Re, Bruno & Pailos, Federico

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