Predicativity, the Russell-Myhill Paradox, and Church's Intensional Logic

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church's intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms of Church's intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin's intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions.Comment: Forthcoming in The Journal of Philosophical Logi

CAOVerif : an open-source deductive verification platform for cryptographic software implementations

CAO is a domain-specific imperative language for cryptography, offering a rich mathematical type system and crypto-oriented language constructions. We describe the design and implementation of a deductive verification platform for CAO and demonstrate that the development time of such a complex verification tool could be greatly reduced by building on the Jessie plug-in included in the Frama-C framework. We discuss the interesting challenges raised by the domain-specific characteristics of CAO, and describe how we tackle these problems in our design. We base our presentation on real-world examples of CAO code, extracted from the open-source code of the NaCl cryptographic library, and illustrate how various cryptography-relevant security properties can be verified.This work was supported by Project Best Case, co-financed by the North Portugal Regional Operational Programme (ON.2 – O Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF)

Functional HDLs : a historical overview

When designing hardware systems, a variety of models and languages are available whose aim is to manage complexity by allowing specification of such systems at different abstraction levels. Languages such as Verilog and VHDL where designed with simulation in mind rather than synthesis and lack features such as parametrised complex circuit definitions, a must for the design of generic complex systems. A more modern approach is the use of functional languages for hardware description that take advantage of the inherent abstraction in this paradigm, resulting in a more concise and manageable description of the system. This paper gives an overview of different functional language implementations for hardware description, highlighting their historical significance in terms of their capabilities and design approach. We will compare and contrast different ways that certain features, such as circuit sharing, have been implemented in these.peer-reviewe

Optimizing and Incrementalizing Higher-order Collection Queries by AST Transformation

In modernen, universellen Programmiersprachen sind Abfragen auf Speicher-basierten Kollektionen oft rechenintensiver als erforderlich. Während Datenbankenabfragen vergleichsweise einfach optimiert werden können, fällt dies bei Speicher-basierten Kollektionen oft schwer, denn universelle Programmiersprachen sind in aller Regel ausdrucksstärker als Datenbanken. Insbesondere unterstützen diese Sprachen meistens verschachtelte, rekursive Datentypen und Funktionen höherer Ordnung. Kollektionsabfragen können per Hand optimiert und inkrementalisiert werden, jedoch verringert dies häufig die Modularität und ist oft zu fehleranfällig, um realisierbar zu sein oder um Instandhaltung von entstandene Programm zu gewährleisten. Die vorliegende Doktorarbeit demonstriert, wie Abfragen auf Kollektionen systematisch und automatisch optimiert und inkrementalisiert werden können, um Programmierer von dieser Last zu befreien. Die so erzeugten Programme werden in derselben Kernsprache ausgedrückt, um weitere Standardoptimierungen zu ermöglichen. Teil I entwickelt eine Variante der Scala API für Kollektionen, die Staging verwendet um Abfragen als abstrakte Syntaxbäume zu reifizieren. Auf Basis dieser Schnittstelle werden anschließend domänenspezifische Optimierungen von Programmiersprachen und Datenbanken angewandt; unter anderem werden Abfragen umgeschrieben, um vom Programmierer ausgewählte Indizes zu benutzen. Dank dieser Indizes kann eine erhebliche Beschleunigung der Ausführungsgeschwindigkeit gezeigt werden; eine experimentelle Auswertung zeigt hierbei Beschleunigungen von durchschnittlich 12x bis zu einem Maximum von 12800x. Um Programme mit Funktionen höherer Ordnung durch Programmtransformation zu inkrementalisieren, wird in Teil II eine Erweiterung der Finite-Differenzen-Methode vorgestellt [Paige and Koenig, 1982; Blakeley et al., 1986; Gupta and Mumick, 1999] und ein erster Ansatz zur Inkrementalisierung durch Programmtransformation für Programme mit Funktionen höherer Ordnung entwickelt. Dabei werden Programme zu Ableitungen transformiert, d.h. zu Programmen die Eingangsdifferenzen in Ausgangdifferenzen umwandeln. Weiterhin werden in den Kapiteln 12–13 die Korrektheit des Inkrementalisierungsansatzes für einfach-getypten und ungetypten λ-Kalkül bewiesen und Erweiterungen zu System F besprochen. Ableitungen müssen oft Ergebnisse der ursprünglichen Programme wiederverwenden. Um eine solche Wiederverwendung zu ermöglichen, erweitert Kapitel 17 die Arbeit von Liu and Teitelbaum [1995] zu Programmen mit Funktionen höherer Ordnung und entwickeln eine Programmtransformation solcher Programme im Cache-Transfer-Stil. Für eine effiziente Inkrementalisierung ist es weiterhin notwendig, passende Grundoperationen auszuwählen und manuell zu inkrementalisieren. Diese Arbeit deckt einen Großteil der wichtigsten Grundoperationen auf Kollektionen ab. Die Durchführung von Fallstudien zeigt deutliche Laufzeitverbesserungen sowohl in Praxis als auch in der asymptotischen Komplexität.In modern programming languages, queries on in-memory collections are often more expensive than needed. While database queries can be readily optimized, it is often not trivial to use them to express collection queries which employ nested data and first-class functions, as enabled by functional programming languages. Collection queries can be optimized and incrementalized by hand, but this reduces modularity, and is often too error-prone to be feasible or to enable maintenance of resulting programs. To free programmers from such burdens, in this thesis we study how to optimize and incrementalize such collection queries. Resulting programs are expressed in the same core language, so that they can be subjected to other standard optimizations. To enable optimizing collection queries which occur inside programs, we develop a staged variant of the Scala collection API that reifies queries as ASTs. On top of this interface, we adapt domain-specific optimizations from the fields of programming languages and databases; among others, we rewrite queries to use indexes chosen by programmers. Thanks to the use of indexes we show significant speedups in our experimental evaluation, with an average of 12x and a maximum of 12800x. To incrementalize higher-order programs by program transformation, we extend finite differencing [Paige and Koenig, 1982; Blakeley et al., 1986; Gupta and Mumick, 1999] and develop the first approach to incrementalization by program transformation for higher-order programs. Base programs are transformed to derivatives, programs that transform input changes to output changes. We prove that our incrementalization approach is correct: We develop the theory underlying incrementalization for simply-typed and untyped λ-calculus, and discuss extensions to System F. Derivatives often need to reuse results produced by base programs: to enable such reuse, we extend work by Liu and Teitelbaum [1995] to higher-order programs, and develop and prove correct a program transformation, converting higher-order programs to cache-transfer-style. For efficient incrementalization, it is necessary to choose and incrementalize by hand appropriate primitive operations. We incrementalize a significant subset of collection operations and perform case studies, showing order-of-magnitude speedups both in practice and in asymptotic complexity

A semantic Bayesian network for automated share evaluation on the JSE

Advances in information technology have presented the potential to automate investment decision making processes. This will alleviate the need for manual analysis and reduce the subjective nature of investment decision making. However, there are different investment approaches and perspectives for investing which makes acquiring and representing expert knowledge for share evaluation challenging. Current decision models often do not reflect the real investment decision making process used by the broader investment community or may not be well-grounded in established investment theory. This research investigates the efficacy of using ontologies and Bayesian networks for automating share evaluation on the JSE. The knowledge acquired from an analysis of the investment domain and the decision-making process for a value investing approach was represented in an ontology. A Bayesian network was constructed based on the concepts outlined in the ontology for automatic share evaluation. The Bayesian network allows decision makers to predict future share performance and provides an investment recommendation for a specific share. The decision model was designed, refined and evaluated through an analysis of the literature on value investing theory and consultation with expert investment professionals. The performance of the decision model was validated through back testing and measured using return and risk-adjusted return measures. The model was found to provide superior returns and risk-adjusted returns for the evaluation period from 2012 to 2018 when compared to selected benchmark indices of the JSE. The result is a concrete share evaluation model grounded in investing theory and validated by investment experts that may be employed, with small modifications, in the field of value investing to identify shares with a higher probability of positive risk-adjusted returns

Higher-Order Contingentism, Part 1: Closure and Generation

This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to the view itself, do not exist to be drawn. The paper begins with a non-technical exposition of the main ideas and technical results, which can be read on its own. This exposition is followed by a formal investigation of higher-order contingentism, in which the tools of variable-domain intensional model theory are used to articulate various versions of the view, understood as theories formulated in a higher-order modal language. Our overall assessment is mixed: higher-order contingentism can be fleshed out into an elegant systematic theory, but perhaps only at the cost of abandoning some of its original motivations

The notion of dimension in geometry and algebra

This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are invoked and compared.Comment: 29 pages, a revie

Articulating design-time uncertainty with DRUIDE

Les modélisateurs rencontrent souvent des incertitudes sur la manière de concevoir un modèle logiciel particulier. Les recherches existantes ont montré comment les modélisateurs peuvent travailler en présence de ce type d' ''incertitude au moment de la conception''. Cependant, le processus par lequel les développeurs en viennent à exprimer leurs incertitudes reste flou. Dans cette thèse, nous prenons des pas pour combler cette lacune en proposant de créer un langage de modélisation d'incertitude et une approche pour articuler l'incertitude au moment de la conception. Nous illustrons notre proposition sur un exemple et l'évaluons non seulement sur deux scénarios d'ingénierie logicielle, mais aussi sur une étude de cas réel basée sur les incertitudes causées par la pandémie COVID-19. Nous menons également un questionnaire post-étude avec les chercheurs qui ont participé à l'étude de cas. Afin de prouver la faisabilité de notre approche, nous fournissons deux outils et les discutons. Enfin, nous soulignons les avantages et discutons des limites de notre travail actuel.Modellers often encounter uncertainty about how to design a particular software model. Existing research has shown how modellers can work in the presence of this type of ''design-time uncertainty''. However, the process by which developers come to elicit and express their uncertainties remains unclear. In this thesis, we take steps to address this gap by proposing to create an uncertainty modelling language and an approach for articulating design-time uncertainty. We illustrate our proposal on a worked example and evaluate it not only on two software engineering scenarios, but also on a real case study based on uncertainties caused by the COVID-19 pandemic. We also conduct a post-study questionnaire with the researchers who participated in the case study. In order to prove the feasibility of our approach, we provide two tool supports and discuss them. Finally, we highlight the benefits and discuss the limitations of our current work

Onto Collab: Strategic review oriented collaborative knowledge modeling using ontologies

Modeling efficient knowledge bases for improving the semantic property of the World Wide Web is mandatory for promoting innovations and developments in World Wide Web. There is a need for efficient and organized modeling of the knowledge bases. In this paper, a strategy Onto Collab is proposed for construction of knowledge bases using ontology modeling. Ontologies are visualized as the basic building blocks of the knowledge in the web. The cognitive bridge between the human conceptual understanding of real world data and the processable data by computing systems is represented by Ontologies. A domain is visualized as a collection of similar ontologies. A review based strategy is proposed over a secure messaging system to author ontologies and a platform for retracing the domain ontologies as individuals and as a team is proposed. Evaluations for ontologies constructed pertaining to a domain for non-wiki knowledge bases is carried out