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We propose an architecture for storing visual expressions within an environment which supports various forms of visual expression editing, like syntax directed editing, free editing, and layout editing. The proposed architecture syntax graph represents the logical structure of a visual expression in terms of its visual language syntax; a spatial relations graph represents the pictorial structure of a visual expression with graphical objects as nodes and spatial relations as edges. We explain the distinction between the two ways of structuring in detail, we show how coupled graph grammars can be used to define, build and relate the two structures, and we explain how an editor for a visual language can be defined on top of these data structures.

The effective use of visual languages requires a precise understanding of their meaning. Moreover, it is impossible to prove properties of visual languages like soundness of transformation rules or correctness results without having a formal language definition. Although this sounds obvious, it is surprising that only little work has been done about the semantics of visual languages, and even worse, there is no general framework available for the semantics specification of different visual languages. We present such a framework that is based on a rather general notion of abstract visual syntax. This framework allows a logical as well as a denotational approach to visual semantics, and it facilitates the formal reasoning about visual languages syntax and semantics for the visual languages VEX, Show and Tell, and Euler Circles. We demonstrate the semantics in action by proving a rule for visual reasoning with Euler Circles and by showing the correctness of a Show and Tell program.

Diagrams are always used when communicating complex situations. Diagram editors support the user when editing diagrams on a computer. However, creating diagram editors is expensive and time-consuming. Frameworks that can be customized for the specific diagram classes considerably reduce these costs. In previous work, the framework DiaGen using an internal hypergraph model and offering syntax-directed editing had been introduced. This paper presents an incremental hypergraph parser and an extension of DiaGen that allows for editing diagrams like in a drawing tool. The hypergraph parser detects correct (sub-) diagrams online and notifies the user of incorrect diagram parts. This allows editing with temporally inconsistent diagrams which supports a natural editing style.

This paper addresses issues in visual language theory with the help of logic formalisms that were developed for reasoning tasks by the artificial intelligence and spatial databases community, especially for spatial and diagrammatical reasoning. We describe an approach based on three formal components. Topology is used to define basic geometric objects. Theory about spatial relations from the domain of spatial databases is employed to define possible relationships between visual language elements. Description logic theory from the AI community is used to combine topology and spatial relations. The resulting theory has been successfully applied to formally specifying semantics of visual languages. The theory’s application is illustrated with a specification of entity-relationship diagrams. 1

With the prevalence of graph data in a variety of domains, there is an increasing need for a language to query and manipulate graphs with heterogeneous attributes and structures. We propose a query language for graph databases that supports arbitrary attributes on nodes, edges, and graphs. In this language, graphs are the basic unit of information and each query manipulates one or more collections of graphs. To allow for flexible compositions of graph structures, we extend the notion of formal languages from strings to the graph domain. We present a graph algebra extended from the relational algebra in which the selection operator is generalized to graph pattern matching and a composition operator is introduced for rewriting matched graphs. Then, we investigate access methods of the selection operator. Pattern matching over large graphs is challenging due to the NP-completeness of subgraph isomorphism. We address this by a combination of techniques: use of neighborhood subgraphs and profiles, joint reduction of the search space, and optimization of the search order. Experimental results on real and synthetic large graphs demonstrate that our graph specific optimizations outperform an SQL-based implementation by orders of magnitude.

We describe the object-oriented editor GenEd supporting the design of specifications for visual notations. Prominent features of GenEd are (1) it is generic, i.e. domain-specific syntax and semantics are specified by users; (2) built-in parser for actual drawings, driven by formal specifications; (3) powerful reasoning capabilities about diagrams and their specification. GenEd’s specification language is based on a fully formalized theory for describing visual notations. Three examples, place-transition petri nets, entity-relationship diagrams, and a small GIS application are presented.

Studies have shown significant benefits of the use of Domain-Specific Languages. However, designing a DSL still seems to be an art, rather than a craft following a clear methodology. In this paper, we discuss a first step towards a methodology for designing such languages. The presented approach, which is referred to as the Language-Driven Approach, is rooted in formal techniques and independent of accepted software engineering process models. We illustrate the approach with a small and instructive case study.

When working with diagrams in visual environments like graphical diagram editors, diagrams have to be represented by an internal model. Graphs and hypergraphs are well-known concepts for such internal models. This paper shows how hypergraphs can be uniformly used for a wide range of different diagram types where hyperedges are used to represent diagram components as well as spatial relationships between components. This paper also proposes a procedure for translating diagrams into their hypergraph model, i.e., a graphical scanner, and a procedure to check the hypergraph against a hypergraph grammar defining the diagrams' syntax, i.e., a parsing procedure. Such procedures are necessary to make use of such a hypergraph model in visual environments that support free-hand editing where the user can modify diagrams arbitrarily.

We consider the representation of a visual specification within a highly integrated environment which provides specialized support for the associated visual language. We state that such an environment needs to represent a visual specification at four levels in order to perform its tasks: (1) the physical layout, (2) the pictorial structure, (3) the abstract structure, and (4) the representation of the meaning. Furthermore, we will show how graph grammars, constraint solving, and attribute evaluation can be used to keep the representations up-to-date with each other. It will turn out that defining the structure at different levels and defining the visual syntax are in fact two names for the same thing. 1 INTRODUCTION An important class of visual languages are the so-called diagrammatic visual languages which can be seen as collections of diagrams. Each diagram is composed of graphical objects and has a well-defined meaning. Some examples of frequently used diagrammatic visual languages...