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Towards an embedding of Graph Transformation in Intuitionistic Linear Logic

Research paper by Paolo Torrini, Reiko Heckel

Indexed on: 29 Nov '09Published on: 29 Nov '09Published in: Computer Science - Logic in Computer Science



Abstract

Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified linear logic, leading to a Curry-Howard style isomorphism between graphs and transformations on one hand, formulas and proof terms on the other. With linear implication representing rules and reachability of graphs, and the tensor modelling parallel composition of graphs and transformations, we obtain a language able to encode graph transformation systems and their computations as well as reason about their properties.