Goguen, J.A, Ginali, S. A categorical approach to general systems theory. In G. Klir (ed.), Applied General Systems Research, 1978, 257-270.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....8, 10] and many others and is based on a dynamical systems theory vocabulary. ZS posits algebraic concepts between specification levels, behavior, states, and components. ZS relies on compositionally closed systems of components. The concepts form a natural tie in with categorytheoretic concepts [1, 3, 4, 5, 6, 11]. The history of science and engineering is replete with stories of great advances occurring after notions are examined by new methods for This work was partially supported by the Shodor Computational Science Fund funded by the Shodor Education Foundation, Inc. Durham, NC and NSF Grant ....

....have a complete mechanism for describing systems and then reasoning about them. The ZS approach strongly suggests category theory, with its emphasis on morphisms, as a natural formalization setting. Category theory also played a role in development of General Systems Theory, primarily by Goguen [3, 4, 5, 6]. The usefulness of the categorical approach is that it links ZS and system theory on the one hand to 2 abstract algebra, logic, and theoretical computer science on the other. 3.1. Basic Categories. A category consists of objects obC and arrows arC. There is no fixed notion of what the ....

J. A. Goguen and Suzanna Ginaldi. A categorical approach to general systems theory. In Applied General Systems Research, pages 257--270. Plenum, 1978.

.... process models (e.g. limits in suitable categories characterise parallel composition of processes) and a way of relating different models of concurrency (through adjunctions) Such categorial characterisations bring the field much closer to Goguen s categorial approach to General Systems Theory [Goguen and Ginali 78] and make the semantic domains much easier to institutionalise . Thirdly, the work developed in the IS CORE project (BRA 3023 6071) has investigated categorial techniques on both sides of the satisfaction relation, having built several institutions for object specification based on modal ....

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research, Plenum 1978, 257-270.

....92] the ability to build around temporal theories a semantic domain in which notions of component specification and system configuration can be formalised in a way that mirrors corresponding model theoretic notions for process behaviour. Following Goguen s work on General Systems Theory [Goguen and Ginall 78] the formalisation of such semantic domains can be given using Category Theory: given a category of widgets, the operation of putting a system of widgets together to form some super widget corresponds to taking the (co)limit of the diagram of widgets that shows how to interconnect them . These ....

....studied its properties as a formalism for component specification and system configuration. This characterisation depends on structural properties of the theories of the logic. These structural properties were formalised using Category Theory following Goguen s approach to General Systems Theory [Goguen and Ginall 78] an approach recently echoed in corresponding model theoretic notions for process behaviour [Sassone et al. 93] More specifically, we built an adjunction between two categories that capture different aspects of the formalisation of the notion of process. On the one hand, we defined a category ....

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research, Plenum 1978, 257-270.

.... process models (e.g. limits in suitable categories characterise parallel composition of processes) and a way of relating different models of concurrency (through adjunctions) Such categorial characterisations bring the field much closer to Goguen s categorial approach to General Systems Theory [Goguen and Ginali 78] and make the semantic domains much easier to institutionalise . Thirdly, the work developed in the IS CORE project (BRA 3023 6071) has investigated categorial techniques on both sides of the satisfaction relation, having built several institutions for object specification based on modal ....

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research, Plenum 1978, 257-270.

....of atomic objects. However, one of the requirements of object orientation is the support for operations that allow us to build the description of a more complex object from the description of its components. Formal tools for this purpose can be borrowed from category theory: as stated in [Goguen and Ginali 78] given a category of widgets, the operation of putting a system of widgets together to form a super widget corresponds to taking a colimit of the diagram of widgets that shows how to interconnect them . From the specification point of view, the idea is to use theory presentations as ....

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research, Plenum 1978, 257-270

....directly relevant to the concerns of SA. The specific tools that we have in mind are based on Category Theory, a fairly recent mathematical theory (as far as Mathematics is concerned) and have been developed since the early 70 s by J. Goguen for formalising aspects of General Systems Theory (e.g. [15]) namely the process of building complex systems as interconnections of simpler components Our main objective is to show that, as a mathematical notion, Category Theory (CT) captures much of the spirit and practice that one can recognise in the literature on SA. First of all, one of the ....

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research , Plenum 1978, 257-270.

....92] the ability to build around temporal theories a semantic domain in which notions of component specification and system configuration can be formalised in a way that mirrors corresponding model theoretic notions for process behaviour. Following Goguen s work on General Systems Theory [Goguen and Ginali 78] the formalisation of such semantic domains can be given using Category Theory: given a category of widgets, the operation of putting a system of widgets together to form some super widget corresponds to taking the (co)limit of the diagram of widgets that shows how to interconnect them . These ....

....studied its properties as a formalism for component specification and system configuration. This characterisation depends on structural properties of the theories of the logic. These structural properties were formalised using Category Theory following Goguen s approach to General Systems Theory [Goguen and Ginali 78] an approach recently echoed in corresponding model theoretic notions for process behaviour [Sassone et al. 93] More specifically, we built an adjunction between two categories that capture different aspects of the formalisation of the notion of process. On the one hand, we defined a category ....

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research, Plenum 1978, 257-270.

.... and Maibaum 92] is to adopt theories instead of formulae as building blocks for component specification, using interpretations between theories (theory morphisms) as a means for specifying interconnections between components in the spirit of the categorial approach to systems theory proposed in [Goguen and Ginali 78] However, although theories and interpretations between theories have proved to provide an adequate semantic domain for discussing system specification and design, actual specification design modules are better accounted for in terms of particular (standard) structures of theories, as already ....

....is the ability to start from separate descriptions of how components behave and interconnect these descriptions in order to define how components interact within a system (and form new, larger grain, components) From a formal point of view, and following the direction initiated by J. Goguen [e.g. Goguen and Ginali 78] Category Theory provides a neat formalisation of component interconnection as a means of defining complex systems: given a category of widgets, the operation of putting a system of widgets together to form a super widget corresponds to taking a (co)limit of the diagram of widgets that shows ....

[Article contains additional citation context not shown here]

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research, Plenum 1978, 257-27

.... that given a category of widgets, the operation of putting a system of widgets together to form some super widget corresponds to taking the colimit of the diagram of widgets that shows how to interconnect them [Goguen 89] This dogma first appeared in the context of General Systems Theory [Goguen and Ginali 78] and is applied in this case to specifications of systems rather than mathematical models of systems. This view of the nature of the specification process leads intrinsically to modularity in specification in the sense that the components of a system may be specified separately and later on ....

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research, Plenum 1978, 257-270

....Theory in a universal way. As put forward by Goguen in the context of General Systems Theory, given a category of widgets, the operation of putting a system of widgets together to form a super widget corresponds to taking a colimit of the diagram of widgets that shows how to interconnect them [Goguen and Ginali 78] In order to illustrate how colimits work, we consider first colimits of signature diagrams, in particular the simplest form of colimits: pushouts. Consider the following diagram: 4 q V int = a ; R= G= f a oe a 1 f oe f 1 a oe a 2 f oe f 2 q 1 V 1 int = b 1 ; q 2 V 2 int ....

....that promotes reuse. This idea is supported by the results obtained in several areas of research, namely on the use of Category Theory for formalising process semantics of concurrent systems as in [Sassone et al. 93] the categorical approach to General Systems Theory developed by J. Goguen [e.g. Goguen and Ginali 78] and the categorical approach to Specification Theory developed from institutions [Goguen and Burstall 92] Moreover, functorial relationships have already been established inter and intra formalisms: Sassone et al. 93] use adjunctions to map between different process models, e.g. transition ....

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research , Plenum 1978, 257-270.

....be formally described. The simpleminded view of classes and relations recalled in the first paragraph is clearly not appropriate for capturing systems of interconnected components. Instead, we shall adopt the categorical approach proposed by J. Goguen for General Systems Theory (e.g. Goguen, 1973, Goguen and Ginali, 1978). Capitalising on our recent work on reactive system specification (Fiadeiro and Maibaum, 1992) and parallel program design (Fiadeiro and Maibaum, 1996) we shall view both #### and #### as categories in which systems of interconnected components are modelled through diagrams (in the categorical ....

....logic and the parallel program design language COMMUNITY. THE CATEGORICAL VIEW OF SYSTEMS In the early 70 s, J. Goguen proposed the use of categorical techniques in General Systems Theory for unifying a variety of notions of system behaviour and their composition techniques (Goguen, 1973, Goguen and Ginali, 1978). His approach has been summarised in a very simple but far reaching principle: given a category of widgets, the operation of putting a system of widgets together to form a super widget corresponds to taking a colimit of the diagram of widgets that shows how to interconnect them . In this ....

Goguen, J. and Ginali, S. (1978) A Categorical Approach to General Systems Theory, in G.Klir (ed) Applied General Systems Research, Plenum, 257-270.

.... subclass may be defined through subsorting and interpretations between theories (what in FOOPS [33] corresponds to sub modules) We show how interconnections between objects can be established, namely by specifying which actions they share, following the general categorial principle established in [30] and which suggests that a complex system is explained in terms of a diagram that depicts its components and the way they are interconnected. Finally, in section 5, we outline the Oblog diagrammatic language constructs which allow us to introduce object classes as well as interaction between the ....

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research, Plenum 1978, 257-270

....system can be decomposed, a nice algebraic characterisation of which is provided, for instance, by the theory of processes. The same categorial principle can be applied to such algebraic models of systems as well. In fact, this principle first appeared in the context of General Systems Theory [Goguen and Ginali 78] and has been recently reawakened [eg Goguen 91] in an attempt to provide semantic foundations for concurrent interacting objects, namely using sheaftheory. Other applications of the same principle have been tested, namely for more traditional trace based process models [eg Costa and Sernadas ....

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research, Plenum 1978, 257-270

....that are made on the environment in rely guarantee styles of specification. 1 Introduction In the early 70 s, J. Goguen proposed the use of categorical techniques in General Systems Theory for unifying a variety of notions of system behaviour and their composition techniques [Goguen 71, 73, Goguen and Ginali 78] His approach has been summarised in a very simple but far reaching principle: given a category of widgets, the operation of putting a system of widgets together to form a super widget corresponds to taking a colimit of the diagram of widgets that shows how to interconnect them . These ....

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research, Plenum 1978, 257-270.

....(Standard) ML [50] has also been strongly influenced by this work on Clear. Clear introduced the ideas that a specification module determines a theory, and that such theories can be put together using colimits; these ideas have their origin in some earlier work by Goguen on General Systems Theory [23, 36]. Clear provided operations for summing, renaming, extending, hiding, importing and (in the case of generics) applying theories. Theories in turn denote classes of models. The earliest work that we know giving a calculus of modules is also due to Goguen and Burstall [31] Building on Clear, they ....

Joseph Goguen and Susanna Ginali. A categorical approach to general systems theory. In George Klir, editor, Applied General Systems Research, pages 257--270. Plenum, 1978.

....formally described. The simple minded view of classes and relations recalled in the first paragraph is clearly not appropriate for capturing systems of interconnected components. Instead, we shall adopt the categorical approach proposed by J. Goguen for General Systems Theory (e.g. Goguen, 1973, Goguen and Ginali, 1978). Capitalising on our recent work on reactive system specification (Fiadeiro and Maibaum, 1992) and parallel program design (Fiadeiro and Maibaum, 1996) we shall view both PROG and SPEC as categories in which systems of interconnected components are modelled through diagrams (in the categorical ....

....logic and the parallel program design language COMMUNITY. 2 THE CATEGORICAL VIEW OF SYSTEMS In the early 70 s, J. Goguen proposed the use of categorical techniques in General Systems Theory for unifying a variety of notions of system behaviour and their composition techniques (Goguen, 1973, Goguen and Ginali, 1978). His approach has been summarised in a very simple but far reaching principle: given a category of widgets, the operation of putting a system of widgets together to form a superwidget corresponds to taking a colimit of the diagram of widgets that shows how to interconnect them . In this section, ....

Goguen, J. and Ginali, S. (1978) A Categorical Approach to General Systems Theory, in G.Klir (ed) Applied General Systems Research, Plenum, 257-270.

.... combined using category theoretic operations, in particular, the co limit construction: given a category of widgets, the operation of putting a system of widgets together to form some super widget corresponds to taking the co limit of the diagram of widgets that shows how to interconnect them [10] Using this integration of category theoretic structuring and temporal or modal logics, the development of the Object Calculus has been carried out by research groups at Imperial College and the University of Lisbon over the last 10 years. It has been taken up by other research groups and applied ....

J Goguen and S Ginali, A Categorical Approach to General Systems Theory, in G. Klir (Ed.), Applied General Systems Research, Plenum 1978, pp 257--270.

....of the constructions. The point is not that we are less convinced of the importance of categorial techniques in the study of combinations, of any nature, as shown by a long history of fruitful results (see, for instance, 25] in the lines of the principles advocated in the past by [29]. However, for the purpose of this paper, it seemed that the categorial apparatus would make it too long and, at the same time, somehow deviate the attention of the reader from the main purpose of relating synchronization, parameterization and fibring. In section 2, we shall settle our main ....

J. Goguen and S. Ginali. A categorical approach to general systems theory. In G. Klir, editor, Applied General Systems Research, pages 257--270. Plenum, 1978.

....or two over a 30 years span. That having been said, let me plunge onward. What I have to say in this section relates to mathematics and computing. I do note the philosophy of science had many very interesting developments on the logic of science [48] and continuing development through the 1990s [49]. I have tried to use these ideas in [47] The logical rules for the observed system and the theoretical system are beyond the scope of this discussion. 48. The three classes: observational, theoretical, and calculational. There are three classes of systems to attend to: observational, ....

....Poland, June 1 5, 1999, page submitted, 1999. 48] Frederick Suppe. Introduction and afterword. In Frederick Suppe, editor, The Structure of Scientific Theories: The Search for Philosophic Understanding of Scientific Theories, pages 3 244, 617 730, Urbana, IL, 1977. University of Illinois Press. [49] Patrick Suppes. Models and Methods in the Philosophy of Science. Kluwer Academic, 1993. 50] S. Weerawarana, E.N. Houstis, J.R. Rice, A. Joshi, and C.E. Houstis. Pythia expert system. ACM Trans. Math. Soft. 23:447 468, 1997. 51] Gregory V. Wilson. What should computer scientists teach to ....

Joseph Goguen and Susanna Ginali. A categorical approach to general systems theory. In Applied General Systems Research, pages 257--270. Plenum, 1978.

No context found.

Goguen, J.A, Ginali, S. A categorical approach to general systems theory. In G. Klir (ed.), Applied General Systems Research, 1978, 257-270.

....and that we are not at all dependent upon interleaving. In particular, Lilius [34] has shown how to model Petri nets in our sheaf theoretic framework. This paper builds on a much earlier paper [15] which used sheaf theory as part of a research programme on Categorical General Systems Theory [13, 14, 18]. My interest in this area was revived by the desire to give a semantics for foops (a Functional Object Oriented Programming System) 22, 25] and for the Rewrite Rule Machine, a multi grain hierarchical massively parallel graph rewriting machine (see [19] and [17] The main points made in this ....

....systems, through diagrams and their limits, while the second concerns glueing together behaviour over domains. 3. 3 Interconnection The principles that objects are sheaves, systems are diagrams, and behaviour is limit are all taken from some earlier work in categorical General System Theory [13, 14, 18]. Another principle from this work is that interconnecting systems corresponds to taking colimits in the category of systems, where sharing is indicated by inclusion maps from shared parts into the systems that share them. The papers [13, 14, 18] develop some very general results in this setting, ....

[Article contains additional citation context not shown here]

Joseph Goguen and Susanna Ginali. A categorical approach to general systems theory. In George Klir, editor, Applied General Systems Research, pages 257--270. Plenum, 1978.

....some physical (or conceptual) system, then the limit provides an object which (together with its projection morphisms) represents all possible behaviours of the system that are consistent with the given constraints. This intuition goes back to some work on General System Theory from 1969 74, [16, 27], and has many applications in computing science: 4.1 Products. An early achievement of category theory was to give a precise definition for the notion of product, which was previously known in many special cases, but only understood vaguely as a general concept. The definition is due to Mac ....

....say widgets, then the result of interconnecting a system of widgets to form a super widget corresponds to taking the colimit of the diagram of widgets in which the morphisms show how they are interconnected. At least for me, this intuition arose in the context of General Systems Theory [16, 27]. It may be interesting to note that the duality between the categorical definitions of limits and colimits suggests a similar duality between the intuitive notions of solution and interconnection. Now some examples: 6.1 Putting Theories together to make Specifications. Complexity is a fundamental ....

Joseph Goguen and Susanna Ginali. A categorical approach to general systems theory. In George Klir, editor, Applied General Systems Research, pages 257-- 270. Plenum, 1978.

....and (pure) Prolog. In [20] it is even extended to imperative programming. Clear introduced the ideas that a specification module determines a theory, and that such theories can be put together using colimits; these ideas have their origin in some earlier work by Goguen on General Systems Theory [19, 27]. Clear provided operations for summing, renaming, extending, hiding, importing and (in the case of generics) applying theories. Theories in turn denote classes of models. The earliest work that we know giving a calculus of modules is also due to Goguen and Burstall [24] Building on Clear, they ....

Joseph Goguen and Susanna Ginali. A categorical approach to general systems theory. In George Klir, editor, Applied General Systems Research, pages 257--270. Plenum, 1978.

No context found.

J.Goguen and S.Ginalli, "A Categorical Approach to General Systems Theory", i n G.Klir(ed),Applied General Systems Research,Plenum1978, 257-270.

No context found.

J.Goguen and S.Ginali, "A Categorical Approach to General Systems Theory", in G.Klir (ed) Applied General Systems Research, Plenum 1978, 257-270.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC