Affiliation:
1. Department of Logic, Faculty of Philosophy, Lomonosov Moscow State University, 119234, Moscow, Russia
Abstract
Abstract
In this work, we propose a variant of so-called informational semantics, a technique elaborated by Voishvillo, for two infectious logics, Deutsch’s ${\mathbf{S}_{\mathbf{fde}}}$ and Szmuc’s $\mathbf{dS}_{\mathbf{fde}}$. We show how the machinery of informational semantics can be effectively used to analyse truth and falsity conditions of disjunction and conjunction. Using this technique, it is possible to claim that disjunction and conjunction can be rightfully regarded as such, a claim which was disputed in the recent literature. Both ${\mathbf{S}_{\mathbf{fde}}}$ and $\mathbf{dS}_{\mathbf{fde}}$ are formalized in terms of natural deduction. This allows us to solve several problems: to develop a natural deduction calculus for ${\mathbf{S}_{\mathbf{fde}}}$ containing the standard form of disjunction elimination (in contrast to the calculus by Petrukhin), to introduce the first natural deduction calculus for $\mathbf{dS}_{\mathbf{fde}}$ and to reflect the fundamental symmetry between ${\mathbf{S}_{\mathbf{fde}}}$ and $\mathbf{dS}_{\mathbf{fde}}$ on proof-theoretical level forming a convenient basis for obtaining their well-known extensions $\mathbf{K}^{\mathbf{w}}_{\mathbf{3}}$ and $\mathbf{PWK}$.
Funder
Russian Science Foundation
Publisher
Oxford University Press (OUP)
Reference45 articles.
1. Begründung einer strengen Implikation;Ackermann;Journal of Symbolic Logic,1956
2. Semantic information;Bar-Hillel;British Journal for the Philosophy of Science,1953
3. Exactly true and non-falsity logics meeting infectious ones;Belikov;Journal of Applied Non-Classical Logics,2020
4. A useful four-valued logic;Belnap,1977
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