Abstract
Abstract In the literature, Weak Kleene logics are usually taken as three-valued logics. However, Suszko has challenged the main idea of many-valued logic claiming that every logic can be presented in a two-valued fashion. In this paper, we provide two-valued semantics for the Weak Kleene logics and for a number of four-valued subsystems of them. We do the same for the so-called Logics of Nonsense, which are extensions of the Weak Kleene logics with unary operators that allow looking at them as Logics of Formal Inconsistency (LFIs) and Logics of Formal Underterminedness (LFUs). Our aim with this work, rather than arguing for Suszko’s thesis, is to show that two-valued presentations of these peculiar logics enlighten the non-standard behavior of their logical connectives. More specifically, the two-valued presentations of paraconsistent logics illustrate and clarify the disjunctive flavor of the conjunction, and dually, the two-valued presentations of paracomplete subsystems of Weak Kleene logics reveal the conjunctive flavor of the disjunction.
Highlights
AND AIMThis paper has three thematic backgrounds: Weak Kleene logics, Logics of Nonsense and Suszko’s Thesis
In the last section we introduced a number of Weak Kleene logics characterized in terms of many-valued semantics
We have provided two-valued semantics to some many-valued logics, and we have analyzed the behaviour of the connectives defined in the resulting systems
Summary
This paper has three thematic backgrounds: Weak Kleene logics, Logics of Nonsense and Suszko’s Thesis. The present investigation represents an attempt to bring Logics of Nonsense closer to the standard formalism entertained when dealing with LFIs and LFUs. the main reason for providing suitable twovalued semantics to Weak Kleene logics is to enlighten some properties of the systems that, we think, are somewhat hidden in their many-valued presentations.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
