Knowledge representation and update in hierarchies of graphs

Harmer, Russ; Oshurko, Eugenia

doi:10.1016/j.jlamp.2020.100559

Cited by 5 publications

(12 citation statements)

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“…In particular, we have presented the construction that composes consecutive SqPO rewrites, provided the first rewrite is reversible. We have also presented the notion of rule hierarchy, that generalizes SqPO rewriting to hierarchies of objects, and allows for an efficient representation of rewriting and its propagation, as previously presented in [16]. We have studied the conditions under which an arbitrary rule hierarchy can be applied to the corresponding hierarchy of objects and described the conditions for such an application to be reversible.…”

Section: Discussionmentioning

confidence: 99%

“…A hierarchy of objects in a category C is a directed acyclic graph (DAG) whose nodes are objects and whose edges are arrows from C such that all paths between each pair of objects are equal [16]. We refer to the latter condition as the commutativity condition.…”

Section: Hierarchies and Sqpo Rewriting In Hierarchiesmentioning

confidence: 99%

“…the representation of knowledge from some concrete graph obtained by moving along alternative paths leading to the same abstract graph is consistent. The propagation framework presented in [16] allows us to transform individual graphs inside a hierarchy and perform the co-evolution of its different layers, which guarantees the consistency of knowledge at all times.…”

Section: Hierarchies and Sqpo Rewriting In Hierarchiesmentioning

confidence: 99%

“…SqPO rewriting enables an efficient representation of object transformations using rules. To be able to build and study such a representation for transformations in hierarchies, let us briefly formulate the notions of rewriting and propagation in hierarchies (formal details can be found in [16]).…”

Section: Hierarchies and Sqpo Rewriting In Hierarchiesmentioning

confidence: 99%

“…Such a rule, called the projection of r + , is constructed given a specification for forward propagation (i.e. a rule factorization and a clean-up arrow [16]), and contains only expansive updates (addition and merging).…”

Section: Expressing Rewriting and Propagation In Hierarchiesmentioning

confidence: 99%

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Reversibility and Composition of Rewriting in Hierarchies

Harmer

Oshurko

2020

Electron. Proc. Theor. Comput. Sci.

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In this paper, we study how graph transformations based on sesqui-pushout rewriting can be reversed and how the composition of rewrites can be constructed. We illustrate how such reversibility and composition can be used to design an audit trail system for individual graphs and graph hierarchies. This provides us with a compact way to maintain the history of updates of an object, including its multiple versions. The main application of the designed framework is an audit trail of updates to knowledge represented by hierarchies of graphs. Therefore, we introduce the notion of rule hierarchy that represents a transformation of the entire hierarchy, study how rule hierarchies can be applied to hierarchies and analyse the conditions under which this application is reversible. We then present a theory for constructing the composition of consecutive hierarchy rewrites. The prototype audit trail system for transformations in hierarchies of simple graphs with attributes is implemented as part of the ReGraph Python library.

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Section: Discussionmentioning

confidence: 99%

Section: Hierarchies and Sqpo Rewriting In Hierarchiesmentioning

confidence: 99%

Section: Hierarchies and Sqpo Rewriting In Hierarchiesmentioning

confidence: 99%

Section: Hierarchies and Sqpo Rewriting In Hierarchiesmentioning

confidence: 99%

Section: Expressing Rewriting and Propagation In Hierarchiesmentioning

confidence: 99%

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