Graph Transformations, Proofs, and Grammars

Graph transformation systems or graph grammars are a generalization of formal grammars used in linguistics.One of principal differences is that the structures that are transformed by transformation rules are no more linear. In this paper we consider graph transformation systems in connection with proof theory. We develop the graph transformation framework, where the attributes are derivable judgments of some deductive system. The computation functions are represented by partial proofs. We consider the application of graph transformation systems to the description of Kleene-style permutation of rules, to the derivations with “distant links”, to “parallel derivations” and “presupposed judgements”. As a “feedback” to linguistics, we discuss applications to the linguistic derivations and their transformations, and some aspects of the notion of “presupposition”.