We present an event structure semantics for contextual nets, an extension of P/T Petri nets where transitions can check for the presence of tokens without consuming them (read-only operations). A basic rôle is played by asymmetric event structures, a generalization of Winskel’s prime event structures where symmetric conflict is replaced by a relation modelling asymmetric conflict or weak causality, used to represent a new kind of dependency between events arising in contextual nets. Extending Winskel’s seminal work on safe nets, the truly concurrent event based semantics of contextual nets is given at categorical level via a chain of coreflections

this paper is to show how a collection of specification constructs may be formally defined that supports the former effort. We should stress that we shall not attempt to provide a full and practical specification language that can be used for object-oriented design. We shall have to limit ourselves to concentrate on the definition of our main primitive of specification (formalising the notion of object) together with two well known specification constructs: inheritance and aggregation (complex objects). However, we do not see deep problems in extending our results to other useful constructs such as class/type grouping and parameterisation.

. The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. We adopt the model-theoretic view of logic as captured in the notions of institution and of parchment (an algebraic way of presenting institutions). We propose a new, modified notion of parchment together with parchment morphisms and representations. In contrast to the original parchment definition and our earlier work, in model-theoretic parchments introduced here the universal semantic structure is distributed over individual signatures and models. We lift formal properties of the categories of institutions and their representations to this level: the category of model-theoretic parchments is complete, and their representations may be put together using categorical limits as well. However, model-theoretic parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessar...

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An object is a unit of structure and behavior; it has an identity which persists through change; objects communicate with each other; they are classified by object types, collected into object classes, related by inheritance, and composed to form complex objects. In the first part of the paper, this rich world of concepts and constructions is explained in an informal but systematic way, independent of any language or system. In the second part, features of an object specification language are outline which incorporate most of these concepts and constructions. 1 Introduction There are many languages, systems, methods and approaches in computing which call themselves "object--oriented", among them object--oriented programming languages like SmallTalk [GR83], C++ [St86] and Eiffel [Me88], object--oriented database systems like GemStone [BOS91], O 2 [De91], IRIS [Fi87] and ORION [Ki88], and object--oriented system development methods like GOOD [SS86], MOOD [Ke88] and HOOD [Hei88]. High--l...

The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. Following Goguen and Burstall, we adopt the model-theoretic view of logic as captured in the notion of institution and of parchment (a certain algebraic way of presenting institutions). We propose a modified notion of parchment together with a notion of parchment morphism and representation, respectively. We lift formal properties of the categories of institutions and their representations to this level: the category of parchments is complete, and parchment representations may be put together using categorical limits as well. However, parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessary invention for proper combination of various logical features may be introduced either on an ad hoc basis (when putting parchments together using limits in the cat...

Term rewriting systems are widely used throughout computer science as they provide an abstract model of computation while retaining a comparatively simple syntax and semantics. In order to reason within large term rewriting systems, structuring operations are used to build large term rewriting systems from smaller ones. Of particular interest is whether key properties are modular, thatis,ifthe components of a structured term rewriting system satisfy a property, then does the term rewriting system as a whole? A body of literature addresses this problem, but most of the results and proofs depend on strong syntactic conditions and do not easily generalize. Although many specific modularity results are known, a coherent framework which explains the underlying principles behind these results is lacking. This thesis posits that part of the problem is the usual, concrete and syntaxoriented semantics of term rewriting systems, and that a semantics is needed which on the one hand elides unnecessary syntactic details but on the other hand still possesses enough expressive power to model the key concepts arising from

View merging, also called view integration, is a key problem in conceptual modeling. Large models are often constructed and accessed by manipulating individual views, but it is important to be able to consolidate a set of views to gain a unified perspective, to understand interactions between views, or to perform various types of end-to-end analysis. View merging is complicated by incompleteness and inconsistency of views. Once views are merged, it is useful to be able to trace the elements of the merged view back to their sources. In this paper, we propose a framework for merging incomplete and inconsistent graph-based views. We introduce a formalism, called poset-annotated graphs, which incorporates a systematic annotation scheme capable of modeling incompleteness and inconsistency as well as providing a built-in mechanism for ownership traceability. We show how structure-preserving maps can capture the relationships between disparate views modeled as poset-annotated graphs, and provide a general algorithm for merging views with arbitrary interconnections. We use the i ∗ modeling language [26] as an example to demonstrate how our approach can be applied to existing graph-based modeling languages, especially in the domain of early Requirements Engineering. 1

. We propose an algebraic characterisation of the notion of coordination in the sense of recently proposed languages and computational models that provide a clear separation between the modelling of individual software components and their interaction in the overall software organisation. We show how this separation can be captured in Goguen's categorical approach to General Systems Theory and borrow examples from specification logics, program design languages, mathematical models of behaviour, and coordination languages to illustrate the applicability of our algebraic characterisation. 1 Introduction Several recently proposed languages and computational models, e.g. those discussed in [4], support the separation between what, in the definition of a system, is responsible for its computational aspects and what is concerned with coordinating the interaction between its different components. As explained in [12]: "(A) computation model allows programmers to build a single computa...

Based on a categorical semantics that has been developed for typed graph grammars we uses colimits (pushouts) to model composition and (reverse) graph grammar morphisms to describe refinements of typed graph grammars. Composition of graph grammars w.r.t. common subgrammars is shown to be compatible with the semantics, i.e. the semantics of the composed grammar is obtained as the composition of the semantics of the component grammars. Moreover, the structure of a composed grammar is preserved during a refinement step in the sense that compatible refinements of the components induce a refinement of the composition. The concepts and results are illustrated by an example. 1 Introduction This contribution addresses the structuring and refinement of typed graph grammars defined according to the algebraic double pushout approach [5]. Typed graph grammars are introduced in [2] for the double pushout approach (cf. [6] for a corresponding notion in the single-pushout setting). They generalize ...