Adaptability Checking in Multi-Level Complex Systems

A hierarchical model for multi-level adaptive systems is built on two basic levels: a lower behavioural level B accounting for the actual behaviour of the system and an upper structural level S describing the adaptation dynamics of the system. The behavioural level is modelled as a state machine and the structural level as a higher-order system whose states have associated logical formulas (constraints) over observables of the behavioural level. S is used to capture the global and stable features of B, by a defining set of allowed behaviours. The adaptation semantics is such that the upper S level imposes constraints on the lower B level, which has to adapt whenever it no longer can satisfy them. In this context, we introduce weak and strong adaptabil- ity, i.e. the ability of a system to adapt for some evolution paths or for all possible evolutions, respectively. We provide a relational characterisation for these two notions and we show that adaptability checking, i.e. deciding if a system is weak or strong adaptable, can be reduced to a CTL model checking problem. We apply the model and the theoretical results to the case study of motion control of autonomous transport vehicles.Comment: 57 page, 10 figures, research papaer, submitte

Event-B in the Institutional Framework: Defining a Semantics, Modularisation Constructs and Interoperability for a Specification Language

Event-B is an industrial-strength specification language for verifying the properties of a given system’s specification. It is supported by its Eclipse-based IDE, Rodin, and uses the process of refinement to model systems at different levels of abstraction. Although a mature formalism, Event-B has a number of limitations. In this thesis, we demonstrate that Event-B lacks formally defined modularisation constructs. Additionally, interoperability between Event-B and other formalisms has been achieved in an ad hoc manner. Moreover, although a formal language, Event-B does not have a formal semantics. We address each of these limitations in this thesis using the theory of institutions. The theory of institutions provides a category-theoretic way of representing a formalism. Formalisms that have been represented as institutions gain access to an array of generic specification-building operators that can be used to modularise specifications in a formalismindependent manner. In the theory of institutions, there are constructs (known as institution (co)morphisms) that provide us with the facility to create interoperability between formalisms in a mathematically sound way. The main contribution of this thesis is the definition of an institution for Event-B, EVT, which allows us to address its identified limitations. To this end, we formally define a translational semantics from Event- B to EVT. We show how specification-building operators can provide a unified set of modularisation constructs for Event-B. In fact, the institutional framework that we have incorporated Event-B into is more accommodating to modularisation than the current state-of-the-art for Rodin. Furthermore, we present institution morphisms that facilitate interoperability between the respective institutions for Event-B and UML. This approach is more generic than the current approach to interoperability for Event-B and in fact, allows access to any formalism or logic that has already been defined as an institution. Finally, by defining EVT, we have outlined the steps required in order to include similar formalisms into the institutional framework. Hence, this thesis acts as a template for defining an institution for a specification language

Domain-Specific Modelling Languages in Bigraphs

Modelling is a ubiquitous activity in human endeavours, and the construction of informatic models of many kinds is the key to understanding and managing the complexity of an increasingly computational world. We advocate the use of domain-specific modelling languages, instantiated within a “tower ” of models, in order to improve the utility of the models we build, and to ease the process of model construction by moving the languages we use to express such models closer to their respective domains. This thesis is concerned with the study of bigraphical reactive systems as a host for domain-specific modelling languages. We present a number of novel technical developments, including a new complete meta-calculus presentation of bigraphical reactive systems, an abstract machine that instantiates to an abstract machine for any instance calculi, and a mechanism for defining declaratively sorting predicates that always give rise to wellbehaved sortings. We explore bigraphical refinement relations that permit formalisation of the relationship between different languages instantiate

Designing precise and flexible graphical modelling languages for software development

Model-driven approaches to software development involve building computerized models of software and the environment in which it is intended to operate. This thesis offers a selection of the author’s work over the last three decades that addresses the design of precise and flexible graphical modelling languages for use in model-driven software development. The primary contributions of this work are: • Syntropy: the first published object-oriented analysis and design (OOAD) method to fully integrate formal and graphical modelling techniques. • The creation of the Object Constraint Language (OCL) and its integration into the Unified Modeling Language (UML) specification. • The identification of requirements and mechanisms for increasing the flexibility of the UML specification. • The design and implementation of tools for implementing graphical Domain Specific Languages (DSLs). The starting point was the author’s experience with formal specification techniques contrasted with the lack of precision of published object-oriented analysis and design methods. This led to a desire to fully integrate these two topics – formal specification and object-orientation - into a coherent discipline. The Syntropy approach, created in 1994 by this author and John Daniels, was the first published complete attempt to do this. Much of the author’s subsequent published work concerns the Unified Modeling Language (UML). UML represented a welcome unification of earlier OOAD approaches, but suffered badly from inflexibility and lack of precision. A significant part of the work included in this thesis addresses the drawbacks of the UML and proposes improvements to the precision of its definition, including through the invention of Object Constraint Language (OCL) and its incorporation into the UML specification, and the consideration of UML as source material for the definition of Domain Specific Languages (DSLs). Several of the author’s published works in this thesis concern mechanisms for the creation of DSLs, both within a UML framework and separately

Ologs: a categorical framework for knowledge representation

In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research.Comment: 38 page

An incremental prototyping methodology for distributed systems based on formal specifications

This thesis presents a new incremental prototyping methodology for formally specified distributed systems. The objective of this methodology is to fill the gap which currently exists between the phase where a specification is simulated, generally using some sequential logical inference tool, and the phase where the modeled system has a reliable, efficient and maintainable distributed implementation in a main-stream object-oriented programming language. This objective is realized by application of a methodology we call Mixed Prototyping with Object-Orientation (in short: OOMP). This is an extension of an existing approach, namely Mixed Prototyping, that we have adapted to the object-oriented paradigm, of which we exploit the flexibility and inherent capability of modeling abstract entities. The OOMP process proceeds as follows. First, the source specifications are automatically translated into a class-based object-oriented language, thus providing a portable and high-level initial implementation. The generated class hierarchy is designed so that the developer may independently derive new sub-classes in order to make the prototype more efficient or to add functionalities that could not be specified with the given formalism. This prototyping process is performed incrementally in order to safely validate the modifications against the semantics of the specification. The resulting prototype can finally be considered as the end-user implementation of the specified software. The originality of our approach is that we exploit object-oriented programming techniques in the implementation of formal specifications in order to gain flexibility in the development process. Simultaneously, the object paradigm gives the means to harness this newly acquired freedom by allowing automatic generation of test routines which verify the conformance of the hand-written code with respect to the specifications. We demonstrate the generality of our prototyping scheme by applying it to a distributed collaborative diary program within the frame of CO-OPN (Concurrent Object-Oriented Petri Nets), a very powerful specification formalism which allows expressing concurrent and non-deterministic behaviours, and which provides structuring facilities such as modularity, encapsulation and genericity. An important effort has also been accomplished in the development or adaptation of distributed algorithms for cooperative symbolic resolution. These algorithms are used in the run-time support of the generated CO-OPN prototypes

Formal Transformations from Graphically-Based Object-Oriented Representations to Theory-Based Specifications

Formal software specification has long been touted as a way to increase the quality and reliability of software; however, it remains an intricate, manually intensive activity. An alternative to using formal specifications is to use graphically-based, semi-formal specifications such as those used in many object-oriented specification methodologies. While semi-formal specifications are generally easier to develop and understand, they lack the rigor and precision of formal specification techniques. The basic premise of this investigation is that formal software specifications can be constructed using correctness preserving transformations from graphically-based object-oriented representations. In this investigation, object-oriented specifications defined using Rumbaugh\u27s Object Modeling Technique (OMT) were translated into algebraic specifications. To ensure the correct translation of graphically-based OMT specifications into their algebraic counterparts, a formal semantics for interpreting OMT specifications was derived and an algebraic model of object-orientation was developed. This model defines how object-oriented concepts are represented algebraically using an object-oriented algebraic specification language O-SLANG. O-SLANG combines basic algebraic specification constructs with category theory operations to capture internal object class structure as well as relationships between classes. Next, formal transformations from OMT specifications to O-SLANG specifications were defined and the feasibility of automating these transformations was demonstrated by the development of a proof-of-concept system

Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki