The Relevant Logic E and Some Close Neighbours: A Reinterpretation

This paper has two aims. First, it sets out an interpretation of the relevant logic E of relevant entailment based on the theory of situated inference. Second, it uses this interpretation, together with Anderson and Belnap’s natural deduc- tion system for E, to generalise E to a range of other systems of strict relevant implication. Routley–Meyer ternary relation semantics for these systems are produced and completeness theorems are proven

Editor's Introduction

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Editorial Preface

This first issue of volume 12 introduces a new format for the Australasian Journal of Logic

Boolean Conservative Extension Results for some Modal Relevant Logics

This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation

Guest editors’ introduction

A logic is said to be paraconsistent if it doesn’t license you to infer everything from a contradiction. To be precise, let |= be a relation of logical consequence. We call |= explosive if it validates the inference rule: {A,¬A} |= B for every A and B. Classical logic and most other standard logics, including intuitionist logic, are explosive. Instead of licensing you to infer everything from a contradiction, paraconsistent logic allows you to sensibly deal with the contradiction

Boolean Conservative Extension Results for some Modal Relevant Logics

This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation

What is a Paraconsistent Logic?

Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively