Reducing the Number of Annotations in a Verification-oriented Imperative Language

Automated software verification is a very active field of research which has made enormous progress both in theoretical and practical aspects. Recently, an important amount of research effort has been put into applying these techniques on top of mainstream programming languages. These languages typically provide powerful features such as reflection, aliasing and polymorphism which are handy for practitioners but, in contrast, make verification a real challenge. In this work we present Pest, a simple experimental, while-style, multiprocedural, imperative programming language which was conceived with verifiability as one of its main goals. This language forces developers to concurrently think about both the statements needed to implement an algorithm and the assertions required to prove its correctness. In order to aid programmers, we propose several techniques to reduce the number and complexity of annotations required to successfully verify their programs. In particular, we show that high-level iteration constructs may alleviate the need for providing complex loop annotations.Comment: 15 pages, 8 figure

Unsorted Functional Translations

AbstractIn this article we first show how the functional and the optimized functional translation from modal logic to many-sorted first-order logic can be naturally extended to the hybrid language H(@,↓). The translation is correct not only when reasoning over the class of all models, but for any first-order definable class. We then show that sorts can be safely removed (i.e., without affecting the satisfiability status of the formula) for frame classes that can be defined in the basic modal language, and show a counterexample for a frame class defined using nominals

Verificación automática de documentos normativos: ¿ficción o realidad?

El desarrollo de toda pieza de software de cierta escala comienza por una etapa que se conoce como especificación, donde se describen las tareas que el software debe realizar. Estas especificaciones tienen en general una inclinación deóntica, pues indican cuáles comportamientos del sistema bajo estudio son permitidos y cuáles no lo son. Siendo un producto humano, suelen contener errores, contradicciones, casos sin cubrir, etc. Dentro de la Ingeniería del Software existen técnicas y herramientas lógico-matemáticas llamadas métodos formales, que analizan esas especificaciones en busca de defectos, de muy difícil hallazgo manual. Tomando como base las similitudes entre la especificación de software y la de las normas legales, este artículo explora la idea de trasladar al terreno legislativo las técnicas y herramientas que han resultado exitosas para verificar software. Además de repasar los antecedentes académicos en la interacción Informática-Derecho, aplicamos algunas de las técnicas mencionadas a un caso de estudio real en el que encontramos “lagunas” que podrían ser abusadas, y proponemos una agenda de investigación para el área.Sociedad Argentina de Informática e Investigación Operativ

Hybrid Layering

Abstract. Many modal-like logics (including some temporal logics, description logics, hybrid logics, etc.) can be seen as fragments of first order logic. As such, a possible approach to automated deduction in these languages would be to implement satisfaction preserving translations and employ state-of-the-art first order theorem provers. As discussed in (Hustadt, Schmidt, and Weidenbach 1998; Areces, Gennari, Heguiabere, and de Rijke 2000) such approaches do not work if naive translations are used. We propose optimized translations for hybrid languages and report on some interesting behavior we encountered during our empirical testing.

Automated reasoning techniques for hybrid logics

Las "lógicas híbridas" extienden a las lógicas modales tradicionales con el poder de describir y razonar sobre cuestiones de identidad, lo cual es clave para muchas aplicaciones. Aunque lógicas modales que hoy llamaríamos "híbridas" pueden rastrearse hasta cuatro décadas atrás, su estudio sistem ático data de fines de la década del '90. Parte de su interés proviene de que llenan un hueco de expresividad importante de las lógicas modales tradicionales. Uno de los temas de esta tesis es el problema de la satisfacibilidad para la lógica híbrida más conocida, denominada H(@;!), y algunas de sus sublógicas. El de la satisfacibilidad es el problema fundamental en razonamiento automático. En el caso de las lógicas híbridas, éste se ha estudiado fundamentalmente a partir del método de tableaux. En esta tesis intentamos completar el panorama del área investigando el problema de la satisfacibilidad para lógicas híbridas usando resolución clásica de primer orden (vía traducciones) y variaciones de un cálculo basado en resolución que opera directamente sobre fórmulas híbridas. Presentamos, en primer lugar, traducciones de complejidad lineal de fórmulas de H(@;!) a lógica de primer orden, que preservan satisfacibilidad. Éstas están concebidas de manera de reducir el espacio de búsqueda de un demostrador automático basado en resolución de primer orden. Luego cambiamos nuestra atención a cálculos que operan directamente sobre fórmulas híbridas. En particular, consideramos el cálculo llamado de"resolución directa". Inspirados por el caso clásico, transformamos este cálculo en uno de resolución ordenada con funciones de selección y probamos que posee la "propiedad de reducción de contraejemplos", de lo cual se deduce que es completo y compatible con el criterio de redundancia estándar. Mostramos también que un refinamiento de este cálculo es un método de decisión para la sublógica decidible H(@). En la última parte de esta tesis, consideramos ciertas formas normales para lógicas híbridas y otras lógicas modales extendidas. En particular nos interesan formas normales donde se garantice que ciertas modalidades no aparecen por debajo de otros operadores modales. Este tipo de transformaciones puede ser aprovechadas en una etapa de preprocesamiento a fin de reducir el número de inferencias requeridas por un demostrador modal. Al intentar expresar estos resultados de extractibilidad de una manera que comprenda también otras lógicas modales extendidas, llegamos a una formulación de la semántica modal basada en un tipo novedoso de modelos definidos de manera coinductiva. Muchas lógicas modales extendidas (incluyendo las lógicas híbridas) pueden verse en términos de clases de modelos coinductivos. De esta manera, resultados que antes debían probarse por separado para cada lenguaje (pero cuyas pruebas eran en general rutinarias) pueden establecerse de manera general.Hybrid logics augment classical modal logics with machinery for describing and reasoning about identity, which is crucial in many settings. Although modal logics we would today call "hybrid" can be traced back to the work of Prior in the 1960's, their systematic study only began in the late 1990's. Part of their interest comes from the fact they fill an important expressivity gap in modal logics. In fact, they are sometimes referred to as "modal logics with equality". One of the unifying themes of this thesis is the satisfiability problem for the arguably best-known hybrid logic, H(@; !), and some of its sublogics. Satisfiability is the basic problem in automated reasoning. In the case of hybrid logics it has been studied fundamentally using the tableaux method. In this thesis we attempt to complete the picture by investigating satisfiability for hybrid logics using first-order resolution (via translations) and variations of a resolution calculus that operates directly on hybrid formulas. We present firstly several satisfiability-preserving, linear-time translations from H(@; !) to first-order logic. These are conceived in a way such that they tend to reduce the search space of a resolution-based theorem prover for first-order logic. notations can be safely ignored. We then move our attention to resolution-based calculi that work directly on hybrid formulas. In particular, we will consider the so-called direct resolution calculus. Inspired by first-order logic resolution, we turn this calculus into a calculus of ordered resolution with selection functions and prove that it possesses the reduction property for counterexamples from which it follows its completeness and that it is compatible with the well-known standard redundancy criterion. We also show that certain refinement of this calculus constitutes a decision procedure for H(@), a decidable fragment of H(@; !). In the last part of this thesis we investigate certain normal forms for hybrid logics and other extended modal logics. We are interested in normal forms where certain modalities can be guaranteed not to occur under the scope of other modal operators. We will see that these kind of transformations can be exploited in a pre-processing step in order to reduce the number of inferences required by a modal prover. In an attempt to formulate these results in a way that encompasses also other extended modal logics, we arrived at a formulation of modal semantics in terms of a novel type of models that are coinductively defined. Many extended modal logics (such as hybrid logics) can be defined in terms of classes of coinductive models. This way, results that had to be proved separately for each difierent language (but whose proofs were known to be mere routine) now can be proved in a general way.Fil:Gorín, Daniel Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Techniques de raisonnement automatique pour les logiques hybrides

Hybrid logics augment classical modal logics with machinery for describing and reasoning about identity, which is crucial in many settings. Although modal logics we would today call ``hybrid'' can be traced back to the work of Prior in the 1960's, their systematic study only began in the late 1990's. Part of their interest comes from the fact they fill an important expressivity gap in modal logics. In fact, they are sometimes referred to as ``modal logics with equality''. One of the unifying themes of this thesis is the satisfiability problem for the arguably best-known hybrid logic, H(@,dwn), and some of its sublogics. Satisfiability is the basic problem in automated reasoning. In the case of hybrid logics it has been studied fundamentally using the tableaux method. In this thesis we attempt to complete the picture by investigating satisfiability for hybrid logics using first-order resolution (via translations) and variations of a resolution calculus that operates directly on hybrid formulas. We present firstly several satisfiability-preserving, linear-time translations from H(@,dwn) to first-order logic. These are conceived in a way such that they tend to reduce the search space of a resolution-based theorem prover for first-order logic. We then move our attention to resolution-based calculi that work directly on hybrid formulas. In particular, we will consider the so-called direct resolution calculus. Inspired by first-order logic resolution, we turn this calculus into a calculus of ordered resolution with selection functions and prove that it possesses the reduction property for counterexamples from which it follows its completeness and that it is compatible with the well-known standard redundancy criterion. We also show that certain refinement of this calculus constitutes a decision procedure for H(@), a decidable fragment of H(@,dwn). In the last part of this thesis we investigate certain normal forms for hybrid logics and other extended modal logics. We are interested in normal forms where certain modalities can be guaranteed not to occur under the scope of other modal operators. We will see that these kind of transformations can be exploited in a pre-processing step in order to reduce the number of inferences required by a modal prover. In an attempt to formulate these results in a way that encompasses also other extended modal logics, we arrived at a formulation of modal semantics in terms of a novel type of models that are coinductively defined. Many extended modal logics (such as hybrid logics) can be defined in terms of classes of coinductive models. This way, results that had to be proved separately for each different language (but whose proofs were known to be mere routine) now can be proved in a general way.Les logiques hybrides accroissent les logiques modales avec des éléments pour décrire et raisonner à propos de l'identité, ce qui est crucial dans certaines situations. Les logiques modales que l'on connaît comme ``hybrides'' aujourd'hui remontent au travaux de Prior dans les années 1960, mais leur étude systématique n'a commencé qu'au bout des années 1990. Elles sont intéressantes en grande partie car elles comblent un manque en matière d'expressivité dans les logiques modales. D'ailleurs, elles sont connues parfois comme des ``logiques modales avec égalité''. L'un des thèmes centraux de cette thèse est le problème de la satisfiabilité pour celle qui est probablement la mieux connue des logiques hybrides: le système H(@,dwn), et pour certaines de ses sous-logiques. La satisfiabilité est le problème fondamental en raisonnement automatique. Dans le cas des logiques hybrides, elle a été étudiée essentiellement par la méthode des tableaux. Dans cette thèse, nous essayons de compléter le panorama en explorant la satisfiabilité des logiques hybrides par d'autres méthodes: la résolution du premier ordre et des variantes de calcul de résolution qui manipulent directement des formules hybrides. Nous présentons un certain nombre de traductions en temps linéaire de H(@,dwn) à la logique de premier ordre qui préservent la satisfiabilité. Elles sont conçues de façon telle qu'elles réduisent l'espace de recherche. Ensuite nous dirigeons notre attention vers les calculs qui manipulent directement des formules hybrides. En particulier, nous considérons le calcul de résolution directe. Inspirés par la résolution du premier ordre, nous transformons ce calcul en un calcul de résolution ordonnée avec des fonctions de sélection, et nous prouvons qu'il a la propriété de réduction des contre-exemples. Nous concluons ainsi qu'il est réfutationnellement complet et qu'il est compatible avec le fameux critère standard de redondance. Nous montrons également qu'une version raffinée de ce calcul constitue un procédure de décision pour H(@), un fragment décidable de H(@,dwn). Dans la dernière partie de cette thèse, nous explorons certaines formes normales des logiques hybrides et d'autres logiques modales étendues. Nous nous intéressons aux formes normales où certaines modalités ne sont jamais présentes dans la portée d'autres opérateurs modaux. Nous montrons qu'il est possible de profiter de ce type de transformations sous la forme d'un prétraitement, dans le but de réduire le nombre d'inférences nécessaires pour un prouveur modal. En nous efforçant de formuler ces résultats en tenant compte d'autres logiques modales étendues, nous arrivons à une formulation de la sémantique modale par un nouveau type de modèles définis de façon coinductif. Plusieurs logiques modales étendues (dont les logiques hybrides) peuvent être définies par des classes de modèles coinductifs. Ainsi, des résultats qui étaient habituellement prouvés séparément pour chaque langage (mais dont la preuve n'était souvent que de routine) peuvent être démontrés d'une façon générale