Automated reasoning for attributed graph properties

Abstract

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 modelling capabilities and to enable analysis. Firstly, we introduce a new logic of attributed graph properties, where the graph 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 part, and the categorical constructions employed only on a lower 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.

Rule-based Graph Repair

“…Proof. The termination of the repair program based on (2) is shown in [8]. The maximal preservation of the repair program P d based on (2) is shown by induction of the length of transformations: We show that, for all transformations t : G ⇒ P d ,g,h H, ∆(g, d).…”

“…Example 9. For the condition c from Example 8, the repairing set is R. 7 For a rule p = L ←֓ K ֒→ R , 8 A program is A-preserving if the dependency relation i of the program is total. If, additionally, the codomain of i is A, the program is a program with interfaces A or short A-program.…”

“…The notion rule-based repair is used in different meanings. In most cases [11,8], a rule set is derived from a set of constraints and a repair algorithm/program is constructed from the rule set. In this paper, a rule set and a condition are given as input and a repair program is constructed from the rule set.…”

“…In Habel and Sandmann 2018 [8], given a proper condition, we derive a rule set from the condition d and construct a repair program using this rule set. The repair program is required to repair all graphs.…”

“…In this paper, we use programs with interface [14] with selection and unselection of parts, instead of markings as in [8]. For simple cases and illustration purposes, marking may be an alternative.…”