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

CHR: A Constructive Relevant Natural-deduction Logic

AbstractIn this paper we develop a natural-deduction logic which is both constructive and relevant. We use a proof-theoretic argument to justify the rules of the logic. The detailed framework we use to develop our system is modeled on that used to develop Martin-Löf's Type Theory