Categories, Allegories, and Circuit Design

Languages based upon binary relations offer an appealing setting for constructing programs from specifications. For example, working with relations rather than functions allows specifications to be more abstract (for example, many programs have a natural specification using the converse operator on relations), and affords a natural treatment of non-determinism in specifications. In this paper we present a novel pictorial interpretation of relational terms as simple pictures of circuits, and a soundness/completeness result that allows relational equations to be proved by pictorial reasoning

A Relational Derivation of a Functional Program

This article is an introduction to the use of relational calculi in deriving programs. Using the relational caluclus Ruby, we derive a functional program that adds one bit to a binary number to give a new binary number. The resulting program is unsurprising, being the standard $quot;column of half-adders$quot;, but the derivation illustrates a number of points about working with relations rather than with functions

Digital myths

Much of the early work on information theory was directed towards the study of the transmission of telegraph signals. These theoretical treatments lend themselves to descriptions of signals as digital phenomena they are much less convenient for dealing with descriptions of signals as analogue phenomena. Although attempts were made to accommodate analogue and digital signals in the same theory the results were elaborate, hard to follow and difficult to apply. Thus there remain incompatibilities between the common theoretical treatments of analogue and digital signals and hence difficulties in framing criteria for the comparison of analogue and digital techniques. In spite of the difficulty of any formalised comparison it is frequently presumed that digital systems offer greater capacity, better quality, better accuracy, versatility, freedom from error and greater realism in the effects they produce. Digital systems have also been strongly supported as candidates for human biological mechanisms and thus by implication are, seen by some, to be natural. These myths about digital systems have breached the engineers's linguistic closures and have become commonplace. With their promise of perfection, digital systems have become symbols of the modern, the progressive and the revolutionary. Engineers caught up in this tide have come to extoll uncritically particular claimed virtues of going digital so that other options are treated as obsolescent . But through its common usage the word digital is losing its discriminating power and trapped in an image of a controllable world it is becoming a metaphor for modernist aesthetic

Introduction to the 28th International Conference on Logic Programming Special Issue

We are proud to introduce this special issue of the Journal of Theory and Practice of Logic Programming (TPLP), dedicated to the full papers accepted for the 28th International Conference on Logic Programming (ICLP). The ICLP meetings started in Marseille in 1982 and since then constitute the main venue for presenting and discussing work in the area of logic programming

On Graph Refutation for Relational Inclusions

We introduce a graphical refutation calculus for relational inclusions: it reduces establishing a relational inclusion to establishing that a graph constructed from it has empty extension. This sound and complete calculus is conceptually simpler and easier to use than the usual ones.Comment: In Proceedings LSFA 2011, arXiv:1203.542

Elsewhere and Otherwise: Introduction to a Symposium on Fredric Jameson’s ‘Allegory and Ideology’

This text introduces the symposium on Fredric Jameson’s Allegory and Ideology (2019), the second volume in his six-part The Poetics of Social Forms. It frames the debate with a brief exploration of some of the figures and problems of allegory that appear across Jameson’s oeuvre, and surveys some of the Marxist conceptualisations of allegory that have shaped Jameson’s approach, as it straddles allegories of the commodity and allegories of utopia. The musical investigation of the nexus of allegory and affect, and the presentation of political allegory as primarily concerned with the disjunction between (national and international) levels are also touched upon as salient dimensions of Jameson’s theorising

McCarthyism and the Id: Forbidden Planet (1956) as a Veiled Criticism of McCarthyism in 1950s America

Many American science fiction films of the 1950s served as political allegories commenting on the post-war fears of the nation. One major fear was the fear of communist infiltration: the Red Scare. In films of this era, the enemy walks as one of us. In most of these films, the alien other, the monster from without, takes on a familiar form. But at the height of all these fears comes the fear of the enemy from within, an enemy that winds up destroying us from the inside out, as can be seen in Forbidden Planet (1956). In this film, a monster from a scientist’s subconscious, an Id Monster, terrorizes a group of human space explorers surveying an extra-terrestrial planet. Sen. Joseph McCarthy, dedicated to uncovering Communists, ruthlessly conducted senate investigations to accuse people of communism wherever he thought he found them. McCarthyism created an Id Monster in America, a monster that haunted the country for years. This Id Monster saw communist threats where there were few, and thrived until McCarthy was brought down just as Dr. Morbius was in Forbidden Planet (1956). This is one of the first films to criticize McCarthyism in America, and I will demonstrate how this film uses filmic means to convey this criticism through dialogue, art direction, mise-en-scène, sound, and other compositional elements. Forbidden Planet (1956) should be read as a veiled criticism of McCarthyism and the Red Scare in 1950s America

A graphical approach to relational reasoning

Relational reasoning is concerned with relations over an unspecified domain of discourse. Two limitations to which it is customarily subject are: only dyadic relations are taken into account; all formulas are equations, having the same expressive power as first-order sentences in three variables. The relational formalism inherits from the Peirce-Schröder tradition, through contributions of Tarski and many others. Algebraic manipulation of relational expressions (equations in particular) is much less natural than developing inferences in first-order logic; it may in fact appear to be overly machine-oriented for direct hand-based exploitation. The situation radically changes when one resorts to a convenient representation of relations based on labeled graphs. The paper provides details of this representation, which abstracts w.r.t. inessential features of expressions. Formal techniques illustrating three uses of the graph representation of relations are discussed: one technique deals with translating first-order specifications into the calculus of relations; another one, with inferring equalities within this calculus with the aid of convenient diagram-rewriting rules; a third one with checking, in the specialized framework of set theory, the definability of particular set operations. Examples of use of these techniques are produced; moreover, a promising approach to mechanization of graphical relational reasoning is outlined