Reflective Relational Machines

AbstractWe propose a model of database programming withreflection(dynamic generation of queries within the host programming language), called thereflective relational machine, and characterize the power of this machine in terms of known complexity classes. In particular, the polynomial time restriction of the reflective relational machine is shown to express PSPACE, and to correspond precisely to uniform circuits of polynomial depth and exponential size. This provides an alternative, logic based formulation of the uniform circuit model, which may be more convenient for problems naturally formulated in logic terms, and establishes that reflection allows for more “intense” parallelism, which is not attainable otherwise (unless P=PSPACE). We also explore the power of the reflective relational machine subject to restrictions on the number of variables used, emphasizing the case of sublinear bounds

Logische Grundlagen von Datenbanktransformationen für Datenbanken mit komplexen Typen

Database transformations consist of queries and updates which are two fundamental types of computations in any databases - the first provides the capability to retrieve data and the second is used to maintain databases in light of ever-changing application domains. With the rising popularity of web-based applications and service-oriented architectures, the development of database transformations must address new challenges, which frequently call for establishing a theoretical framework that unifies both queries and updates over complex-value databases. This dissertation aims to lay down the foundations for establishing a theoretical framework of database transformations in the context of complex-value databases. We shall use an approach that has successfully been used for the characterisation of sequential algorithms. The sequential Abstract State Machine (ASM) thesis captures semantics and behaviour of sequential algorithms. The thesis uses the similarity of general computations and database transformations for characterisation of the later by five postulates: sequential time postulate, abstract state postulate, bounded exploration postulate, background postulate, and the bounded non-determinism postulate. The last two postulates reflect the specific form of transformations for databases. The five postulates exactly capture database transformations. Furthermore, we provide a logical proof system for database transformations that is sound and complete.Datenbanktransformationen sind Anfragen an ein Datenbanksystem oder Modifikationen der Daten des Datenbanksystemes. Diese beiden grundlegenden Arten von Berechnungen auf Datenbanksystemen erlauben zum einem den Zugriff auf Daten und zum anderen die Pflege der Datenbank. Eine theoretische Fundierung von Datenbanktransformationen muss so flexibel sein, dass auch neue web-basierten Anwendungen und den neuen serviceorientierte Architekturen reflektiert sind, sowie auch die komplexeren Datenstrukturen. Diese Dissertation legt die Grundlagen für eine Theoriefundierung durch Datenbanktransformationen, die auch komplexe Datenstrukturen unterstützen. Wir greifen dabei auf einen Zugang zurück, der eine Theorie der sequentiellen Algorithmen bietet. Die sequentielle ASM-These (abstrakte Zustandsmaschinen) beschreibt die Semantik und das Verhalten sequentieller Algorithmen. Die Dissertation nutzt dabei die Gleichartigkeit von allgemeinen Berechnungen und Datenbanktransformationen zur Charakterisierung durch fünf Postulate bzw. Axiome: das Axiom der sequentiellen Ausführung, das Axiom einer abstrakten Charakterisierbarkeit von Zuständen, das Axiom der Begrenzbarkeit von Zustandsänderungen und Zustandssicht, das Axiom der Strukturierung von Datenbanken und das Axiom der Begrenzbarkeit des Nichtdeterminismus. Die letzten beiden Axiome reflektieren die spezifische Seite der Datenbankberechnungen. Die fünf Axiome beschreiben vollständig das Verhalten von Datenbanktransformationen. Weiterhin wird eine Beweiskalkül für Datenbanktransformationen entwickelt, der vollständig und korrekt ist

The Significance of Evidence-based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences

In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines

Topics in Programming Languages, a Philosophical Analysis through the case of Prolog

[EN]Programming languages seldom find proper anchorage in philosophy of logic, language and science. is more, philosophy of language seems to be restricted to natural languages and linguistics, and even philosophy of logic is rarely framed into programming languages topics. The logic programming paradigm and Prolog are, thus, the most adequate paradigm and programming language to work on this subject, combining natural language processing and linguistics, logic programming and constriction methodology on both algorithms and procedures, on an overall philosophizing declarative status. Not only this, but the dimension of the Fifth Generation Computer system related to strong Al wherein Prolog took a major role. and its historical frame in the very crucial dialectic between procedural and declarative paradigms, structuralist and empiricist biases, serves, in exemplar form, to treat straight ahead philosophy of logic, language and science in the contemporaneous age as well. In recounting Prolog's philosophical, mechanical and algorithmic harbingers, the opportunity is open to various routes. We herein shall exemplify some: - the mechanical-computational background explored by Pascal, Leibniz, Boole, Jacquard, Babbage, Konrad Zuse, until reaching to the ACE (Alan Turing) and EDVAC (von Neumann), offering the backbone in computer architecture, and the work of Turing, Church, Gödel, Kleene, von Neumann, Shannon, and others on computability, in parallel lines, throughly studied in detail, permit us to interpret ahead the evolving realm of programming languages. The proper line from lambda-calculus, to the Algol-family, the declarative and procedural split with the C language and Prolog, and the ensuing branching and programming languages explosion and further delimitation, are thereupon inspected as to relate them with the proper syntax, semantics and philosophical élan of logic programming and Prolog

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science

The Significance of Evidence-based Reasoning in Mathematics, Mathematics Education, Philosophy, and the Natural Sciences

In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines