Behavioural and abstractor specifications revisited

In the area of algebraic specification there are two main approaches for defining observational abstraction: behavioural specifications use a notion of observational satisfaction for the axioms of a specification, whereas abstractor specifications define an abstraction from the standard semantics of a specification w.r.t. an observational equivalence relation between algebras. Earlier work by Bidoit, Hennicker, Wirsing has shown that in the case of first-order logic specifications both concepts coincide semantically under mild assumptions. Analogous results have been shown by Sannella and Hofmann for higher-order logic specifications and recently, by Hennicker and Madeira, for specifications of reactive systems using a dynamic logic with binders. In this paper, we bring these results into a common setting: we isolate a small set of characteristic principles to express the behaviour/abstractor equivalence and show that all three mentioned specification frameworks satisfy these principles and therefore their behaviour and abstractor specifications coincide semantically (under mild assumptions). As a new case we consider observational modal logic where observational satisfaction of Hennessy–Milner logic formulae is defined “up to” silent transitions and observational abstraction is defined by weak bisimulation. We show that in this case the behaviour/abstractor equivalence can only be obtained, if we restrict models to weakly deterministic labelled transition systems.publishe

Behavioral equivalence of hidden k-logics: an abstract algebraic approach

This work advances a research agenda which has as its main aim the application of Abstract Algebraic Logic (AAL) methods and tools to the specification and verification of software systems. It uses a generalization of the notion of an abstract deductive system to handle multi-sorted deductive systems which differentiate visible and hidden sorts. Two main results of the paper are obtained by generalizing properties of the Leibniz congruence — the central notion in AAL. In this paper we discuss a question we posed in [1] about the relationship between the behavioral equivalences of equivalent hidden logics. We also present a necessary and sufficient intrinsic condition for two hidden logics to be equivalent

Behavioral institutions and refinements in generalized hidden logics

We investigate behavioral institutions and refinements in the context of the object oriented paradigm. The novelty of our approach is the application of generalized abstract algebraic logic theory of hidden heterogeneous deductive systems (called hidden k-logics) to the algebraic specification of object oriented programs. This is achieved through the Leibniz congruence relation and its combinatorial properties. We reformulate the notion of hidden k-logic as well as the behavioral logic of a hidden k-logic as institutions. We define refinements as hidden signature morphisms having the extra property of preserving logical consequence. A stricter class of refinements, the ones that preserve behavioral consequence, is studied. We establish sufficient conditions for an ordinary signature morphism to be a behavioral refinement. © J.UCS.FCT via UIM

A short overview of Hidden Logic

In this paper we review a hidden (sorted) generalization of k-deductive systems - hidden k-logics. They encompass deductive systems as well as hidden equational logics and inequational logics. The special case of hidden equational logics has been used to specify and to verify properties in program development of behavioral systems within the dichotomy visible vs. hidden data. We recall one of the main applications of this work - the study of behavioral equivalence. Related results are obtained through combinatorial properties of the Leibniz congruence relation. In addition we obtain a few new developments concerning hidden equational logic, namely we present a new characterization of the behavioral consequences of a theory

Closure properties for the class of behavioral models

Hidden k-logics can be considered as the underlying logics of program specification. They constitute natural generalizations of k-deductive systems and encompass deductive systems as well as hidden equational logics and inequational logics. In our abstract algebraic approach, the data structures are sorted algebras endowed with a designated subset of their visible parts, called filter, which represents a set of truth values. We present a hierarchy of classes of hidden k-logics. The hidden k-logics in each class are characterized by three different kinds of conditions, namely, properties of their Leibniz operators, closure properties of the class of their behavioral models, and properties of their equivalence systems. Using equivalence systems, we obtain a new and more complete analysis of the axiomatization of the behavioral models. This is achieved by means of the Leibniz operator and its combinatorial properties. © 2007 Elsevier Ltd. All rights reserved.FCT via UIM

Compositional Behavior Modeling and Formal Validation of Canal System Operations with Finite State Automata

Traditional approaches to the formal analysis of canal system operations focus on performance. However, now that canal system operations are moving toward increased use of automation in their day-to-day operations, there is a strong need for formal analysis of system functionality with respect to correctness of operations. This report describes a compositional approach to the multi-level behavior modeling and formal validation of canal system operations with hierarchies and networks of finite state automata. Models and specifications of behavior are formally designed as labeled transition systems. To avoid the well-known state explosion problem, we develop a new procedure for viewpoint-action-process traceability, thereby allowing parts of a problem not relevant to a specific decision to be removed from consideration. Key features of the methodology are illustrated through development of behavior models and validation procedures for lockset- and system-level concerns in the Panama Canal System

Abordagem algébrica à igualdade observacional

Mestrado em MatemáticaA especificação algébrica de sistemas de software é um importante tópico dos denominados métodos formais de desenvolvimento de software. Neste contexto, modelam-se programas por álgebras e as suas computações por termos, recorrendo-se aos resultados da Álgebra Universal e da Lógica, como ferramentas de verificação e apoio ao processo de implementação. Em grande parte dos trabalhos sobre o tema presentes na literatura, usa-se a Lógica Equacional como lógica de suporte a estes processos. Contudo, esta lógica mostra-se limitada para a especificação de programas Orientados a Objectos, nomeadamente na especificação de programas com dados encapsulados. A separação entre os aspectos internos e externos do sistema induz uma nova perspectiva do conceito de modelação, segundo a qual, um objecto se considera como sendo uma realização correcta do sistema, se satisfaz os seus requisitos observacionalmente, isto é, se os resultados das computações sobre si executadas satisfazem esses requisitos, podendo não os satisfazer em sentido estrito. Seguindo esta linha de ideias, dois objectos de software são considerados equivalentes quando se comportam da mesma forma perante todas as possíveis computações. Este paradigma é denominado por Abordagem Observacional de Sistemas. Uma forma de adequar a Lógica Equacional a esta abordagem, é pela substituição da igualdade estrita pela relação de Igualdade Observacional, segundo a qual dois elementos se consideram iguais quando se comportam da mesma forma perante qualquer computação, isto é, se produzem os mesmos outputs perante as mesmas computações. Neste trabalho estuda-se a abordagem observacional de sistemas segundo diferentes grupos de investigação, com especial atenção aos trabalhos da Lógica Escondida (por Goguen-Rosu), Lógica Comportamental e Observacional (por Bidoit-Hennicker) e da Lógica Algébrica (por Pigozzi- Martins). Um ponto central do texto é a generalização do processo de desenvolvimento de software por Refinamento Passo-a-Passo a este paradigma. Aprofundam-se aqui algumas variantes deste tópico, incluindo o caso onde se admitem encapsulamentos e desencapsulamentos de dados durante o processo de refinamento. Numa primeira fase do texto o assunto é apresentado ao nível mais geral das especificações algébricas estruturadas (e não exclusivamente do caso das especificações flat) e das igualdades comportamentais (congruências parciais arbitrárias). ABSTRACT: The algebraic specification of software systems is an important topic of socalled formal methods of software development. In this context, programmes are modelled by algebras and computations executed over them by terms, using up the results from Universal Algebra and Logic, as verification and support tools for the implementation process. In a large majority of the works about this subject, it uses the Equational Logic as support logic for these processes. However, this logic is too restrictive for the specification of objectoriented programs, namely, in the programs specification with encapsulated data. The split between the internal and external aspects of the system, induces a new perspective of the modelling concept, whereby an object is considered a correct realization of the system if satisfies observationally their requirements, that is, if the results of computations over it executed satisfies these requirements and being able not to satisfy them in the strict sense. Following this principle, two software objects are considered equivalent when behave the same way at all possible computations. This paradigm is called Observational Approach of Systems. One way to adjust the Equational Logic to the observational approach is by replacing the strict equality by the relation of Observational Equality, according to which two elements are considered equal when behave the same way at the same computations, i.e., if they produce the same outputs before the same computations. We follow this approach according to different research groups, with special attention to the work of Behavioural and Observational Logic (by Bidoit- Hennicker), the Hidden Logic (by Goguen-Rosu) and Abstract Algebraic Logic (by Pigozzi-Martins). A central point of the text is the generalization of the software development process by stepwise refinement to this paradigm. Here some variants of this topic are explored including the case where encapsulated and desencapsulated data are allowed during the refinement process. In a first stage of the text, the subject is presented to a more general level of structured specifications (and not exclusively the case of flat specifications) and the Behavioural Equalities (arbitrary partial congruence)

Hiding More of Hidden Algebra

This paper generalizes the hidden algebra approach to allow: (P1) operations with multiple hidden arguments, and (P2) defining behavioral equivalence with a subset of operations, in addition to the already present (P3) built-in data types, (P4) nondeterminism, (P5) concurrency, and (P6) non-congruent operations. All important results generalize, but more elegant formulations use the new institution in Section 5. Behavioral satisfaction appeared 1981 in [20], hidden algebra 1989 in [9], multiple hidden arguments 1992 in [1], congruent and behavioral operations in [1, 18], behavioral equivalence defined by a subset of operations in [1], and non-congruent operations in [5]; all this was previously integrated in [21], but this paper gives new examples, institutions, and results relating hidden algebra to information hiding. We assume familiarity with basics of algebraic specification, e.g., [11, 13]