On effective linearly ordered sets of comparison functions

Both the existence and the non-existence of a linearly ordered (by certain natural order relations) effective set of comparison functions (=dense comparison classes) are compatible with the ZFC axioms of set theory.

Assignment methods for incidence calculus

Incidence calculus is a mechanism for probabilistic reasoning in which sets of possible worlds, called incidences, are associated with axioms, and probabilities are then associated with these sets. Inference rules are used to deduce bounds on the incidence of formulae which are not axioms, and bounds for the probability of such a formula can then be obtained. In practice an assignment of probabilities directly to axioms may be given, and it is then necessary to find an assignment of incidence which will reproduce these probabilities. We show that this task of assigning incidences can be viewed as a tree searching problem, and two techniques for performing this research are discussed. One of these is a new proposal involving a depth first search, while the other incorporates a random element. A Prolog implementation of these methods has been developed. The two approaches are compared for efficiency and the significance of their results are discussed. Finally we discuss a new proposal for applying techniques from linear programming to incidence calculus.

The outflow ranking method for weighted directed graphs

A ranking method assigns to every weighted directed graph a (weak) ordering of the nodes. In this paper we axiomatize the ranking method that ranks the nodes according to their outflow using four independent axioms. Besides the well-known axioms of anonymity and positive responsiveness we introduce outflow monotonicity – meaning that in pairwise comparison between two nodes, a node is not doing worse in case its own outflow does not decrease and the other node’s outflow does not increase – and order preservation – meaning that adding two weighted digraphs such that the pairwise ranking between two nodes is the same in both weighted digraphs, then this is also their pairwise ranking in the ‘sum’ weighted digraph. The outflow ranking method generalizes the ranking by outdegree for directed graphs, and therefore also generalizes the ranking by Copeland score for tournaments.

A general framework for measuring inconsistency through minimal inconsistent sets

Hunter and Konieczny explored the relationships between measures of inconsistency for a belief base and the minimal inconsistent subsets of that belief base in several of their papers. In particular, an inconsistency value termed MIVC, defined from minimal inconsistent subsets, can be considered as a Shapley Inconsistency Value. Moreover, it can be axiomatized completely in terms of five simple axioms. MinInc, one of the five axioms, states that each minimal inconsistent set has the same amount of conflict. However, it conflicts with the intuition illustrated by the lottery paradox, which states that as the size of a minimal inconsistent belief base increases, the degree of inconsistency of that belief base becomes smaller. To address this, we present two kinds of revised inconsistency measures for a belief base from its minimal inconsistent subsets. Each of these measures considers the size of each minimal inconsistent subset as well as the number of minimal inconsistent subsets of a belief base. More specifically, we first present a vectorial measure to capture the inconsistency for a belief base, which is more discriminative than MIVC. Then we present a family of weighted inconsistency measures based on the vectorial inconsistency measure, which allow us to capture the inconsistency for a belief base in terms of a single numerical value as usual. We also show that each of the two kinds of revised inconsistency measures can be considered as a particular Shapley Inconsistency Value, and can be axiomatically characterized by the corresponding revised axioms presented in this paper.

Mandated prevention in child welfare: Considerations from a framework shaping ethical inquiry

Summary: This article outlines a framework for approaching ethical dilemmas arising from the development, evaluation and implementation of child welfare policies. As such, it is relevant to policy-makers, social researchers and social workers. The central tenets of the framework are developed by drawing on ideas from moral philosophy and critical social theory. These ideas are presented as axioms, theorems and corollaries, a format which has been employed in the social sciences to offer a rational justification for a set of claims. • Findings: This process of reasoning leads to four principle axioms that are seen to shape the ethical scrutiny of social policy: 1) problematizing knowledge; 2) utilizing structured forms of inquiry to enhance understanding; 3) engendering enabling communication with those affected by the ethical concern; and 4) enhancing self-awareness. • Applications: The four axioms are then applied, by way of example, to the current and contentious, 'third way' policy of mandated prevention in child welfare, where the aim is to obviate deleterious outcomes in later life. It is argued that the framework can be applied beyond this specific concern to other pressing, ethical challenges in child welfare.

Advances in the Design of the Oyster Wave Energy Converter

This short paper, structured in 3 distinct sections will touch on some of the key features of the Oyster wave energy device and its recent development. The first section discusses the nature of the resource in the nearshore environment,
some common misunderstandings in relation to it and its suitability for exploitation of commercial wave energy. In the second section a brief description of some of the fundamentals governing flap type devices is given. This serves to emphasise core differences between the Oyster device and other devices. Despite the simplicity of the design and the operation of the device itself, it is shown that Oyster occupies a theoretical space which is substantially outside most established theories and axioms in wave energy. The third section will give a short summary of the recent developments in the design of the Oyster 2 project and touch on how its enhanced features deal with some of the key commercial and technical challenges present in the sector.

Towards a general framework for information fusion

Depending on the representation setting, different combination rules have been proposed for fusing information from distinct sources. Moreover in each setting, different sets of axioms that combination rules should satisfy have been advocated, thus justifying the existence of alternative rules (usually motivated by situations where the behavior of other rules was found unsatisfactory). These sets of axioms are usually purely considered in their own settings, without in-depth analysis of common properties essential for all the settings. This paper introduces core properties that, once properly instantiated, are meaningful in different representation settings ranging from logic to imprecise probabilities. The following representation settings are especially considered: classical set representation, possibility theory, and evidence theory, the latter encompassing the two other ones as special cases. This unified discussion of combination rules across different settings is expected to provide a fresh look on some old but basic issues in information fusion.

Eliciting and estimating valid subjective probabilities: An experimental investigation of the Exchangeability Method.

Using a laboratory experiment, we investigate whether incentive compatibility affects subjective probabilities elicited via the exchangeability method (EM), an elicitation technique consisting of several chained questions. We hypothesize that subjects who are aware of the chaining strategically behave and provide invalid subjective probabilities, while subjects who are not aware of the chaining state their real beliefs and provide valid subjective probabilities. The validity of subjective probabilities is investigated using de Finetti's notion of coherence, under which probability estimates are valid if and only if they obey all axioms of probability theory.
Four experimental treatments are designed and implemented. Subjects are divided into two initial treatment groups: in the first, they are provided with real monetary incentives, and in the second, they are not. Each group is further sub-divided into two treatment groups, in the first, the chained structure of the experimental design is made clear to the subjects, while, in the second, the chained structure is hidden by randomizing the elicitation questions.
Our results suggest that subjects provided with monetary incentives and randomized questions provide valid subjective probabilities because they are not aware of the chaining which undermines the incentive compatibility of the exchangeability method.

'That Puissant City': John Milton's Roman Sojourns 1638-1639

John Milton’s sojourns in Rome (1638-9) are attested by his comments in Defensio Secunda, by the minutes of the English College, by Latin encomia which he received from Roman academicians, and, not least, by his Latin letter to Lucas Holstenius (19/29 March 1639), and several Latin poems which he composed in the course of his residency in the capital city: Ad Salsillum, and three Latin epigrams extolling the praises of the virtuosa soprano, Leonora Baroni. Read together, these texts serve to reveal much about Milton’s participation in, and reaction to, the ‘Puissant City’, (History of Britain, Bk 2).

The present monograph presents fresh evidence of Milton's integration into the academic and cultural life of seventeenth-century Rome. It argues that his links with two Roman academies: the Accademia dei Fantastici and Accademia degli Umoristi constitute a sustained participation in an academic community paralleling that of his independently attested performance in Florentine academies (on which I have published extensively). It also investigates his links with Alessandro Cherubini, David Codner, Giovanni Batista Doni, and the Baroni circle hymned in three published anthologies.

Chapter 1: Milton and the Accademia dei Fantastici investigates the cultural climate surrounding Milton's Ad Salsillum by examining two of that academy's publications: the Poesie dei Signori Accademici Fantastici di Roma (Rome, 1637) and the Academia Tenuta da Fantastici a. 12 di Maggio 1655 (Rome, 1655), the latter celebrating the creation of Fabio Chigi as Pope Alexander VII on 5 April 1655. Read in a new light, Milton’s self-fashioning, it is argued, takes its place not only alongside Salzilli’s encomium in Milton's honour, and his Italian sonnets in the 1637 Poesie, but also in relation to other poems in that collection, and the academy's essentially Catholic eulogistic trend. The chapter also provides fresh evidence of Salzilli’s survival of the illness described in Milton’s poem by his epistolary correspondence with Tomaso Stigliani.

Chapter 2: Milton and the Vatican argues for links between Milton’s Latin letter to Holstenius and a range of Holstenius’ published works: his edition of the axioms of the later Pythagoreans gifted by him to Milton, and his published neo-Platonic works. This is achieved by mutual appropriation of Similitudes in a series of Miltonic similes, the anabasis/katabasis motifs in a reworking of the Platonic theory of the transmigration of souls, and allusion to etymological details highlighted in Holstenius’ published editions. The chapter also reveals Milton’s alertness to typographical procedures and, by association, to Holstenius’ recent role (1638) as Director of the press of the Biblioteca Vaticana.

Chapter 3: Milton and the Accademia degli Umoristi argues for Milton’s likely participation in this Roman academy, as suggested by his links with its members. His three Latin epigrams in praise of Leonora Baroni, the only female member of the Umoristi, have hitherto been studied in relation to the 1639 Applausi in her honour. In a new reading, Milton, it is suggested, invokes and interrogates Catholic doctrine before a Catholic audience only to view the whole through the lens of a neo-Platonic Hermeticism (by echoing the phraseology of the sixteenth-century Franciscan Hannibal Rosselli) that refreshingly transcends religious difference. Crucially, the hitherto neglected L’Idea della Veglia (Rome, 1640) includes further encomiastic verse, sonnets to, and by Leonora, and details of the conversazioni hosted by her family at the precise time of Milton’s Roman sojourns. Milton may well have been a participant. The chapter concludes in an assessment of his links with the youthful prodigy Alessandro Cherubini, and of his audience with Francesco Barberini.

Chapter 4: Milton at a Roman Opera analyses the potential impact of ‘Chi Soffre, Speri’, which he attended on 18/28 February 1639, mounted by Francesco Barberini to inaugurate the recently completed theatre of the Palazzo Barberini. A detailed analysis of the opera's libretto, music, and theatricality casts a backward glance to Milton's Comus, and a forward glance to Paradise Lost. It also assesses Milton’s musical interests at this time, as attested by his links with Doni, and his purchase of works by Monteverdi and others.

Chapter 5: Milton’s English Connections in Rome develops the work of Miller and Chaney by investigating Milton’s co-diners at the English College in Rome on 30 October 1638, and by analysing his links between David Codner (alias Matteo Selvaggio), and the family of Jane Savage, Marchioness of Winchester, lamented by Milton in 1631. It also assesses his potential relations with the Englishman Thomas Gawen, who ‘accidentally sometimes fell into the company of John Milton’ (Antony Wood).