A model characterising strong normalisation for Klop’s extension of λ-calculus is presented. The main technical tools for this result are an inductive definition of strongly normalising terms of Klop’s calculus and an intersection type system for terms of Klop’s calculus.

We characterise the strongly normalising terms of a composition-free calculus of explicit substititions (with or without garbage collection) by means of an intersection type assignment system. The main novelty is a new cut-rule which allows to forget the context of the minor premise when the context of the main premise does not have an assumption for the cut variable.

A rewrite sequence is said to be outermost-fair if every out-ermost redex occurrence is eventually eliminated. O'Donnell has shown that outermost-fair rewriting is normalising for almost orthogonal rst-order term rewriting systems. In this paper we extend this result to the higher-order case.

We prove a folklore theorem, that two derivations in a cut-free sequent calculus for intuitionistic propositional logic (based on Kleene’s G3) are inter-permutable (using a set of basic “permutation reduction rules” derived from Kleene’s work in 1952) iff they determine the same natural deduction. The basic rules form a confluent and weakly normalising rewriting system. §

We introduce a method for establishing that a reduction strategy is normalising and minimal, or dually, that it is perpetual and maximal, in the setting of abstract rewriting. While being complete, the method allows to reduce these global properties to the verification of local diagrams. We show its usefulness both by giving uniform proofs of some known results and by establishing new ones.

PURPOSE To extend our previous research demonstrating that linguistic/interactional features in patients' talk can assist the challenging differential diagnosis of epilepsy and psychogenic nonepileptic seizures (PNES) by exploring the differential diagnostic potential of references to non co-present persons (third parties). METHOD Initial encounters were recorded between 20 seizure patients (...

Corpora of Early Modern English have been collected and released for research for a number of years. With large scale digitisation activities gathering pace in the last decade, much more historical textual data is now available for research on numerous topics including historical linguistics and conceptual history. We summarise previous research which has shown that it is necessary to map histo...