A graph-semantics of business configurations

In this paper we give graph-semantics to a fundamental part of the semantics of the service modeling language SRML. To achieve this goal we develop a new graph transformation system for what we call 2-level symbolic graphs. These kind of graphs extend symbolic graphs with a simple 2-level hierarchy that can be generalized to arbitrary hierarchies. We formalize the semantics using this new graph transformation system using a simple example of a trip booking agent.Postprint (published version

Symbolic Attributed Graphs for Attributed Graph Transformation

In this paper we present a new approach to deal with attributed graphs and attributed graph transformation. This approach is based on working with what we call symbolic graphs, which are graphs labelled with variables together with a formula that constrains the possible values that we may assign to these variables. In particular, in this paper we will compare in detail this new approach with the standard approach to attributed graph transformation

A logic of graph conditions extended with paths

In this paper we tackle the problem of extending the logic of nested graph conditions with paths. This means, for instance, that we may state properties about the existence of paths between some given nodes. As a main contribution, a sound and complete tableau method is defined for reasoning about this kind of properties.Peer ReviewedPostprint (published version

Towards a navigational logic for graphical structures

One of the main advantages of the Logic of Nested Conditions, defined by Habel and Pennemann, for reasoning about graphs, is its generality: this logic can be used in the framework of many classes of graphs and graphical structures. It is enough that the category of these structures satisfies certain basic conditions. In a previous paper [14], we extended this logic to be able to deal with graph properties including paths, but this extension was only defined for the category of untyped directed graphs. In addition it seemed difficult to talk about paths abstractly, that is, independently of the given category of graphical structures. In this paper we approach this problem. In particular, given an arbitrary category of graphical structures, we assume that for every object of this category there is an associated edge relation that can be used to define a path relation. Moreover, we consider that edges have some kind of labels and paths can be specified by associating them to a set of label sequences. Then, after the presentation of that general framework, we show how it can be applied to several classes of graphs. Moreover, we present a set of sound inference rules for reasoning in the logic.Peer ReviewedPostprint (author's final draft

Checking bisimilarity for attributed graph transformation

Borrowed context graph transformation is a technique developed by Ehrig and Koenig to define bisimilarity congruences from reduction semantics defined by graph transformation. This means that, for instance, this technique can be used for defining bisimilarity congruences for process calculi whose operational semantics can be defined by graph transformation. Moreover, given a set of graph transformation rules, the technique can be used for checking bisimilarity of two given graphs. Unfortunately, we can not use this ideas to check if attributed graphs are bisimilar, i.e. graphs whose nodes or edges are labelled with values from some given data algebra and where graph transformation involves computation on that algebra. The problem is that, in the case of attributed graphs, borrowed context transformation may be infinitely branching. In this paper, based on borrowed context transformation of what we call symbolic graphs, we present a sound and relatively complete inference system for checking bisimilarity of attributed graphs. In particular, this means that, if using our inference system we are able to prove that two graphs are bisimilar then they are indeed bisimilar. Conversely, two graphs are not bisimilar if and only if we can find a proof saying so, provided that we are able to prove some formulas over the given data algebra. Moreover, since the proof system is complex to use, we also present a tableau method based on the inference system that is also sound and relatively complete.Postprint (published version

A Framework of hierarchical graphs and its application to the semantics of SRML

Hierarchical grapsh or, in general, hierarchical graph structures are needed when describing visual models at different levels of abstraction. This is the case of the semantic model of SRML, the service modeling language of the european project SENSORIA. In particular, the state model of this language is considered at two level of abstraction. Roughly, at the lowest level, a state configuration is a graph consisting of interconnected components and, at the highest level, business configurations are graphs consisting of interconnected activities, where each activity is a graph of components. Then, a state configuration is the flattening of the corresponding business configuration. Following these ideas, in this paper, we present a new framework of hierarchical graphs, showing that it is m-adhesive. Then we show how this framework can be used to define (part of) a graph transformation semantics of SRML.Postprint (published version

Symbolic model generation for graph properties

Graphs are ubiquitous in Computer Science. For this reason, in many areas, it is very important to have the means to express and reason about graph properties. In particular, we want to be able to check automatically if a given graph property is satisfiable. Actually, in most application scenarios it is desirable to be able to explore graphs satisfying the graph property if they exist or even to get a complete and compact overview of the graphs satisfying the graph property. We show that the tableau-based reasoning method for graph properties as introduced by Lambers and Orejas paves the way for a symbolic model generation algorithm for graph properties. Graph properties are formulated in a dedicated logic making use of graphs and graph morphisms, which is equivalent to first-order logic on graphs as introduced by Courcelle. Our parallelizable algorithm gradually generates a finite set of so-called symbolic models, where each symbolic model describes a set of finite graphs (i.e., finite models) satisfying the graph property. The set of symbolic models jointly describes all finite models for the graph property (complete) and does not describe any finite graph violating the graph property (sound). Moreover, no symbolic model is already covered by another one (compact). Finally, the algorithm is able to generate from each symbolic model a minimal finite model immediately and allows for an exploration of further finite models. The algorithm is implemented in the new tool AutoGraph.Peer ReviewedPostprint (author's final draft

A Semantics of Business Configurations Using Symbolic Graphs

In this paper we give graph-semantics to a fundamental part of the semantics of the service modeling language SRML: business configurations. To achieve this goal we use symbolic graph transformation systems. We formalize the semantics using this graph transformation system and illustrating it with a simple running example of a trip booking agent.Peer Reviewe

Automated reasoning for attributed graph properties

Graphs are ubiquitous in computer science. Moreover, in various application fields, graphs are equipped with attributes to express additional information such as names of entities or weights of relationships. Due to the pervasiveness of attributed graphs, it is highly important to have the means to express properties on attributed graphs to strengthen modeling capabilities and to enable analysis. Firstly, we introduce a new logic of attributed graph properties, where the graph part and attribution part are neatly separated. The graph part is equivalent to first-order logic on graphs as introduced by Courcelle. It employs graph morphisms to allow the specification of complex graph patterns. The attribution part is added to this graph part by reverting to the symbolic approach to graph attribution, where attributes are represented symbolically by variables whose possible values are specified by a set of constraints making use of algebraic specifications. Secondly, we extend our refutationally complete tableau-based reasoning method as well as our symbolic model generation approach for graph properties to attributed graph properties. Due to the new logic mentioned above, neatly separating the graph and attribution parts, and the categorical constructions employed only on a more abstract level, we can leave the graph part of the algorithms seemingly unchanged. For the integration of the attribution part into the algorithms, we use an oracle, allowing for flexible adoption of different available SMT solvers in the actual implementation. Finally, our automated reasoning approach for attributed graph properties is implemented in the tool AutoGraph integrating in particular the SMT solver Z3 for the attribute part of the properties. We motivate and illustrate our work with a particular application scenario on graph database query validation.Peer ReviewedPostprint (author's final draft