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Logic Journal of IGPL Advance Access originally published online on August 10, 2009
Logic Journal of IGPL 2009 17(6):631-696; doi:10.1093/jigpal/jzp026
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Modelling evolvable component systems

Part I: A logical framework

Howard Barringer

School of Computer Science, University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
E-mail: howard.barringer{at}manchester.ac.uk

Dov Gabbay

Department of Computer Science, Kings College London, The Strand, London, WC2R 2LS, UK.
E-mail: dov.gabbay{at}kcl.ac.uk

David Rydeheard

School of Computer Science, University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
E-mail: david.rydeheard{at}manchester.ac.uk


  Abstract

We develop a logical modelling approach to describe evolvable computational systems. In this account, evolvable systems are built hierarchically from components where each component may have an associated supervisory process. The supervisor's purpose is to monitor and possibly change its associated component. Evolutionary change may be determined purely internally from observations made by the supervisor or may be in response to external change. Supervisory processes may be present at any level in the component hierarchy allowing us to use evolutionary behaviour as an integral part of system design.

We model such systems in a revision-based first-order logical framework in which supervisors are modelled as theories which are at a logical meta-level to the theories of their components. This enables evolutionary change of the component to be induced by revision-based changes of the supervisor at the meta-level. In this way, the intervention required in evolutionary change is modelled purely logically.

The hierarchical component-based structure is fairly intricate so we present the basic ideas firstly in a simple setting, the well-known blocks world, before introducing tree-based structures to represent component hierarchies. We also introduce some techniques for establishing the behaviour of evolvable systems specified in this logical framework. The ideas and concepts are driven by example throughout. We conclude with a more substantial example, that of a simple model of an evolvable system of automated bank teller machines.

Key Words: Evolvable Systems • Logical Frameworks • Reconfigurable Component Systems • Revision-Based Logic • Minimum Models

Received for publication 26 April 2007.
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