Many logics in the relevant family can be given a proof theory in the style of Belnap's display logic Belnap 1982. However, as originally given, the proof theory is essentially more expressive than… (More)

This paper continues the work of Priest and Sylvan in Simplified Semantics for Basic Relevant Logics, a paper on the simplified semantics of relevant logics, such as B + and B. We show that the… (More)

The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.

Here is a familiar history: modal logics (see [13]) were around for some time before a semantic framework was found for them (by Kripke and others).1 This framework did at least two Very Good Things… (More)

We are pluralists about logical consequence [1]. We hold that there is more than one sense in which arguments may be deductively valid, that these senses are equally good, and equally deserving of… (More)

This paper generalises Girard's results which embed intuitionistic logic into linear logic by showing how arbitrary substructural logics can be embedded into weaker substructural logics, using a… (More)

This paper is an exercise in formal and philosophical logic. I will show how intuitionistic propositional logic can be extended with a new two-place connective, not expressible in the traditional… (More)

In his paper “Generalised Ortho Negation” [2] J. Michael Dunn mentions a claim of mine to the effect that there is no condition on ‘perp frames’ equivalent to the holding of double negation… (More)

The hallowed path from language to universals has been by way of the correspondence theory of truth: the doctrine that whenever something is true, there must be something in the world which makes it… (More)