An Institutional Framework for Heterogeneous Formal Development in UML

We present a framework for formal software development with UML. In contrast to previous approaches that equip UML with a formal semantics, we follow an institution based heterogeneous approach. This can express suitable formal semantics of the different UML diagram types directly, without the need to map everything to one specific formalism (let it be first-order logic or graph grammars). We show how different aspects of the formal development process can be coherently formalised, ranging from requirements over design and Hoare-style conditions on code to the implementation itself. The framework can be used to verify consistency of different UML diagrams both horizontally (e.g., consistency among various requirements) as well as vertically (e.g., correctness of design or implementation w.r.t. the requirements)

Satisfiability Calculus: An Abstract Formulation of Semantic Proof Systems

The theory of institutions, introduced by Goguen and Burstall in 1984, can be thought of as an abstract formulation of model theory. This theory has been shown to be particularly useful in computer science, as a mathematical foundation for formal approaches to software construction. Institution theory was extended by a number of researchers, José Meseguer among them, who, in 1989, presented General Logics, wherein the model theoretical view of institutions is complemented by providing (categorical) structures supporting the proof theory of any given logic. In other words, Meseguer introduced the notion of proof calculus as a formalisation of syntactical deduction, thus ?implementing? the entailment relation of a given logic. In this paper we follow the approach initiated by Goguen and introduce the concept of Satisfiability Calculus. This concept can be regarded as the semantical counterpart of Meseguer?s notion of proof calculus, as it provides the formal foundations for those proof systems that resort to model construction techniques to prove or disprove a given formula, thus ?implementing? the satisfiability relation of an institution. These kinds of semantic proof methods have gained a great amount of interest in computer science over the years, as they provide the basic means for many automated theorem proving techniques.Fil: Lopez Pombo, Carlos Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Castro, Pablo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; ArgentinaFil: Aguirre, Nazareno M.. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; ArgentinaFil: Maibaum, Thomas S.E.. Mc Master University; Canad

Heterogeneous Theories and the Heterogeneous Tool Set

Heterogeneous multi-logic theories arise in different contexts: they are needed for the specification of large software systems, as well as for mediating between different ontologies. This is because large theories typically involve different aspects that are best specified in different logics (like equational logics, description logics, first-order logics, higher-order logics, modal logics), but also because different formalisms are in practical use (like RDF, OWL, EML). Using heterogeneous theories, different formalims being developed at different sites can be related, i.e. there is a formal interoperability among languages and tools. In many cases, specialized languages and tools have their strengths in particular aspects. Using heterogeneous theories, these strengths can be combined with comparably small effort. By contrast, a true combination of all the involved logics into a single logic would be too complex (or even inconsistent) in many cases. We propose to use emph{institutions} as a formalization of the notion of logical system. Institutions can be related by so-called institution morphsims and comorphisms. Any graph of institutions and (co)morphisms can be flattened to a so-called emph{Grothendieck institution}, which is kind of disjoint union of all the logics, enriched with connections via the (co)morphisms. This semantic basis for heterogeneous theories is complemented by the heterogeneous tool set, which provides tool support. Based on an object-oriented interface for institutions (using type classes in Haskell), it implements the Grothendieck institution and provides a heterogeneous parser, static analysis and proof support for heterogeneous theories. This is based on parsers, static analysers and proof support for the individual institutions, and on a heterogeneous proof calculus for theories in the Grothendieck institution. See also the Hets web page: http://www.tzi.de/cofi/het

Proof Support for Common Logic

We present an extension of the Heterogeneous Tool Set HETS that enables proof support for Common Logic. This is achieved via logic translations that relate Common Logic and some of its sublogics to already supported logics and automated theorem proving systems. We thus provide the first full theorem proving support for Common Logic, including the possibility of verifying meta-theoretical relationships between Common Logic theories

Architectural Refinement in HETS

The main objective of this work is to bring a number of improvements to the Heterogeneous Tool Set HETS, both from a theoretical and an implementation point of view. In the first part of the thesis we present a number of recent extensions of the tool, among which declarative specifications of logics, generalized theoroidal comorphisms, heterogeneous colimits and integration of the logic of the term rewriting system Maude. In the second part we concentrate on the CASL architectural refinement language, that we equip with a notion of refinement tree and with calculi for checking correctness and consistency of refinements. Soundness and completeness of these calculi is also investigated. Finally, we present the integration of the VSE refinement method in HETS as an institution comorphism. Thus, the proof manangement component of HETS remains unmodified

Encoding hybridised institutions into first order logic

"First published online: 12 November 2014"A ‘hybridization’ of a logic, referred to as the base logic, consists of developing the characteristic features of hybrid logic on top of the respective base logic, both at the level of syntax (i.e. modalities, nominals, etc.) and of the semantics (i.e. possible worlds). By ‘hybridized institutions’ we mean the result of this process when logics are treated abstractly as institutions (in the sense of the institution theory of Goguen and Burstall). This work develops encodings of hybridized institutions into (many-sorted) first order logic (abbreviated FOL) as a ‘hybridization’ process of abstract encodings of institutions into FOL, which may be seen as an abstraction of the well known standard translation of modal logic into first order logic. The concept of encoding employed by our work is that of comorphism from institution theory, which is a rather comprehensive concept of encoding as it features encodings both of the syntax and of the semantics of logics/institutions. Moreover we consider the so-called theoroidal version of comorphisms that encode signatures to theories, a feature that accommodates a wide range of concrete applications. Our theory is also general enough to accomodate various constraints on the possible worlds semantics as well a wide variety of quantifications. We also provide pragmatic sufficient conditions for the conservativity of the encodings to be preserved through the hybridization process, which provides the possibility to shift a formal verification process from the hybridized institution to FOL.We thank both Till Mossakowski and Andrzej Tarlecki for the technical suggestion of using the predicates D. The work of the first author has been supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0439. The work of the second author was funded by the European Regional Development Fund through the COMPETE Programme, and by the Portuguese Foundation for Science and Technology through the projects FCOMP-01-0124-FEDER-028923 and NORTE-01-0124-FEDER-000060

Asymmetric Combination of Logics is Functorial: A Survey

Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a given base logic. These examples are surveyed in the paper under a particular perspective—that this sort of combination of logics possesses a functorial nature. Such a view gives rise to several interesting questions. They range from the problem of combining translations (between logics), to that of ensuring property preservation along the process, and the way different asymmetric combinations can be related through appropriate natural transformations