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

Refinement Modal Logic

In this paper we present {\em refinement modal logic}. A refinement is like a bisimulation, except that from the three relational requirements only `atoms' and `back' need to be satisfied. Our logic contains a new operator 'all' in addition to the standard modalities 'box' for each agent. The operator 'all' acts as a quantifier over the set of all refinements of a given model. As a variation on a bisimulation quantifier, this refinement operator or refinement quantifier 'all' can be seen as quantifying over a variable not occurring in the formula bound by it. The logic combines the simplicity of multi-agent modal logic with some powers of monadic second-order quantification. We present a sound and complete axiomatization of multi-agent refinement modal logic. We also present an extension of the logic to the modal mu-calculus, and an axiomatization for the single-agent version of this logic. Examples and applications are also discussed: to software verification and design (the set of agents can also be seen as a set of actions), and to dynamic epistemic logic. We further give detailed results on the complexity of satisfiability, and on succinctness

A reconstruction of the multipreference closure

The paper describes a preferential approach for dealing with exceptions in KLM preferential logics, based on the rational closure. It is well known that the rational closure does not allow an independent handling of the inheritance of different defeasible properties of concepts. Several solutions have been proposed to face this problem and the lexicographic closure is the most notable one. In this work, we consider an alternative closure construction, called the Multi Preference closure (MP-closure), that has been first considered for reasoning with exceptions in DLs. Here, we reconstruct the notion of MP-closure in the propositional case and we show that it is a natural variant of Lehmann's lexicographic closure. Abandoning Maximal Entropy (an alternative route already considered but not explored by Lehmann) leads to a construction which exploits a different lexicographic ordering w.r.t. the lexicographic closure, and determines a preferential consequence relation rather than a rational consequence relation. We show that, building on the MP-closure semantics, rationality can be recovered, at least from the semantic point of view, resulting in a rational consequence relation which is stronger than the rational closure, but incomparable with the lexicographic closure. We also show that the MP-closure is stronger than the Relevant Closure.Comment: 57 page

Semantic model-driven development of web service architectures.

Building service-based architectures has become a major area of interest since the advent of Web services. Modelling these architectures is a central activity. Model-driven development is a recent approach to developing software systems based on the idea of making models the central artefacts for design representation, analysis, and code generation. We propose an ontology-based engineering methodology for semantic model-driven composition and transformation of Web service architectures. Ontology technology as a logic-based knowledge representation and reasoning framework can provide answers to the needs of sharable and reusable semantic models and descriptions needed for service engineering. Based on modelling, composition and code generation techniques for service architectures, our approach provides a methodological framework for ontology-based semantic service architecture

Symbolic reactive synthesis

In this thesis, we develop symbolic algorithms for the synthesis of reactive systems. Synthesis, that is the task of deriving correct-by-construction implementations from formal specifications, has the potential to eliminate the need for the manual—and error-prone—programming task. The synthesis problem can be formulated as an infinite two-player game, where the system player has the objective to satisfy the specification against all possible actions of the environment player. The standard synthesis algorithms represent the underlying synthesis game explicitly and, thus, they scale poorly with respect to the size of the specification. We provide an algorithmic framework to solve the synthesis problem symbolically. In contrast to the standard approaches, we use a succinct representation of the synthesis game which leads to improved scalability in terms of the symbolically represented parameters. Our algorithm reduces the synthesis game to the satisfiability problem of quantified Boolean formulas (QBF) and dependency quantified Boolean formulas (DQBF). In the encodings, we use propositional quantification to succinctly represent different parts of the implementation, such as the state space and the transition function. We develop highly optimized satisfiability algorithms for QBF and DQBF. Based on a counterexample-guided abstraction refinement (CEGAR) loop, our algorithms avoid an exponential blow-up by using the structure of the underlying symbolic encodings. Further, we extend the solving algorithms to extract certificates in the form of Boolean functions, from which we construct implementations for the synthesis problem. Our empirical evaluation shows that our symbolic approach significantly outperforms previous explicit synthesis algorithms with respect to scalability and solution quality.In dieser Dissertation werden symbolische Algorithmen für die Synthese von reaktiven Systemen entwickelt. Synthese, d.h. die Aufgabe, aus formalen Spezifikationen korrekte Implementierungen abzuleiten, hat das Potenzial, die manuelle und fehleranfällige Programmierung überflüssig zu machen. Das Syntheseproblem kann als unendliches Zweispielerspiel verstanden werden, bei dem der Systemspieler das Ziel hat, die Spezifikation gegen alle möglichen Handlungen des Umgebungsspielers zu erfüllen. Die Standardsynthesealgorithmen stellen das zugrunde liegende Synthesespiel explizit dar und skalieren daher schlecht in Bezug auf die Größe der Spezifikation. Diese Arbeit präsentiert einen algorithmischen Ansatz, der das Syntheseproblem symbolisch löst. Im Gegensatz zu den Standardansätzen wird eine kompakte Darstellung des Synthesespiels verwendet, die zu einer verbesserten Skalierbarkeit der symbolisch dargestellten Parameter führt. Der Algorithmus reduziert das Synthesespiel auf das Erfüllbarkeitsproblem von quantifizierten booleschen Formeln (QBF) und abhängigkeitsquantifizierten booleschen Formeln (DQBF). In den Kodierungen verwenden wir propositionale Quantifizierung, um verschiedene Teile der Implementierung, wie den Zustandsraum und die Übergangsfunktion, kompakt darzustellen. Wir entwickeln hochoptimierte Erfüllbarkeitsalgorithmen für QBF und DQBF. Basierend auf einer gegenbeispielgeführten Abstraktionsverfeinerungsschleife (CEGAR) vermeiden diese Algorithmen ein exponentielles Blow-up, indem sie die Struktur der zugrunde liegenden symbolischen Kodierungen verwenden. Weiterhin werden die Lösungsalgorithmen um Zertifikate in Form von booleschen Funktionen erweitert, aus denen Implementierungen für das Syntheseproblem abgeleitet werden. Unsere empirische Auswertung zeigt, dass unser symbolischer Ansatz die bisherigen expliziten Synthesealgorithmen in Bezug auf Skalierbarkeit und Lösungsqualität deutlich übertrifft

Refinement Types for Secure Implementations

We present the design and implementation of a typechecker for verifying security properties of the source code of cryptographic protocols and access control mechanisms. The underlying type theory is a λ-calculus equipped with refinement types for expressing pre- and post-conditions within first-order logic. We derive formal cryptographic primitives and represent active adversaries within the type theory. Well-typed programs enjoy assertion-based security properties, with respect to a realistic threat model including key compromise. The implementation amounts to an enhanced typechecker for the general purpose functional language F#; typechecking generates verification conditions that are passed to an SMT solver. We describe a series of checked examples. This is the first tool to verify authentication properties of cryptographic protocols by typechecking their source code. © 2008 IEEE