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We present nine questions related to the concept of negation and, in passing, we refer to connections with the essays in this special issue. The questions were submitted to one of the most eminent logicians who contributed to the theory of negation, Prof. (Jon) Michael Dunn, but, unfortunately, Prof. Dunn was no longer able to answer them. Michael Dunn passed away on 5 April 2021, and the present special issue of Logical Investigations is dedicated to his memory. The questions concern (i) negation-related topics that have particularly interested Michael Dunn or to which he has made important contributions, (ii) some controversial aspects of the logical analysis of the concept of negation, or (iii) simply properties of negation in which we are especially interested. Though sadly and regrettably unanswered by the distinguished scholar who intended to reply, the questions remain and might stimulate answers by other logicians and further research.

This note offers a non-deterministic semantics for mbC1, introduced by Janusz Ciuciura, and establishes soundness and (strong) completeness results with respect to the Hilbert-style proof system. Moreover, based on the new semantics, we briefly discuss an unexplored variant of mbC1 which has a contra-classical flavor.

In this article, we introduce a new two-valued semantics for infectious logics. The main motivation for this semantics stems from the question if conjunctions and disjunctions of infectious logics can be rightfully called conjunction and disjunction. Building on our new semantics, we will happily conclude that this is the case. We will also show that our semantics can capture various expansions of infectious logics.

One of the oldest systems of paraconsistent logic is the set of so-called C-systems of Newton da Costa, and this has been generalized into a family of systems now known as logics of formal inconsistencies by Walter Carnielli, Marcelo Coniglio and João Marcos. The characteristic notion in these systems is the so-called consistency operator which, roughly speaking, indicates how gluts are behaving. One natural question then is to ask if we can let not only gluts but also gaps be around and generalize the notion of consistency into classicality. This is already considered by Andréa Loparić and da Costa in the style of C-systems. The aim of this paper is to develop a family of systems that generalizes the system of Loparić and da Costa which may be called logics of formal classicality.

The present note revisits the joint work of Leonard Goddard and Richard Routley on significance logics with the aim of shedding new light on their understanding by studying them under the lens of recent semantic developments, such as the plurivalent semantics developed by Graham Priest. These semantics allow sentences to receive one, more than one, or no truth-value at all from a given carrier set. Since nonsignificant sentences are taken to be neither true nor false, i.e. truth-value gaps, in this essay we show that with the aid of plurivalent semantics it is possible to straightforwardly instantiate Goddard and Routley's understanding of how the connectives should work within significance logics. Fil: Szmuc, Damián Enrique. Instituto de Investigaciones Filosóficas - Sadaf; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Filosofía y Letras; Argentina Fil: Omori, Hitoshi. Kyoto University; Japón

A world is trivial if it makes every proposition true all at once. Such a world is impossible, an absurdity. Our world, we hope, is not an absurdity. It is important, nevertheless, for semantic and metaphysical theories that we be able to reason cogently about absurdities—if only to see that they are absurd. In this note we describe methods for ‘observing’ absurd objects like the trivial world without falling in to incoherence, using some basic techniques from modal logic. The goal is to begin to locate the trivial world’s relative position in modal space; the outcome is that the less we assume about relative possibility, the more detail we can discern at the edge of reason.