There are, at first blush, two kinds of construction involved: constructions of proofs of some proposition and constructions of objects of some type. But I will argue that, from the point of view of foundations of mathematics, there is no difference between the two notions. A proposition may be regarded as a type of object, namely, the type of its proofs. Conversely, a type Amay be regarded as ...

Abstractive summarisation is not yet common amongst today’s deployed and research systems. Most existing systems either extract sentences or compress individual sentences. In this paper, we present a summariser that works by a different paradigm. It is a further development of an existing summariser that has an incremental, proposition-based content selection process but lacks a natural languag...

In this paper we describe an experiment in which MANIFOLD is used to coordinate the interprocess communication in a parallelized proposition solver. MANIFOLD is very well suited for applications involving dynamic process creation and dynamically changing (ir)regular communication patterns among sets of independent concurrent cooperating processes. The idea in this case study is simple. The prop...

Any modern approach to a Marxist theory of culture must begin by considering the proposition of a determining base and a determined superstructure. From a strictly theoretical point of view this is not, in fact, where we might choose to begin.1 It would be in many ways preferable if we could begin from a proposition which originally was equally central, equally authentic: namely the proposition...

The precise formulation of PP requires some notation. Let Ch be a function that assigns a number in the interval [0,1] to each proposition A. is the proposition that Ch assigns the chance x to A. Let Cr be a function that assigns a number in the interval [0,1] to each proposition A, corresponding to a person’s degree of belief (or credence) in A. Finally, let E be any proposition. W...

In this work, an erratum for a proposition in the paper ‘‘A New Pre-Order Relation Set Optimization using $\ell$-difference" is outlined. It was pointed out by Stefan Rocktäschel and Ernest Quintana that proof of Proposition 3.11 wrong \cite{koc}. A small detail has been overlooked. new proposition, which closely related to \cite{koc}, presented. The main results are not affected erratum.

• The transitivity theorem, in Proposition 1 of Quickr, has a revision in item iii. The revised version is Proposition 5 in this document. • Definition 1 in Appendix B.2, which defines dominance, has a revision in the condition for c-dominance. The revised version is Definition 1 in this document. We also offer new definitions of equivalence and weak equivalence. • The dominance pushdown rules ...