Towards an embedding of Graph Transformation in Intuitionistic Linear Logic

Towards an embedding of Graph Transformation in Intuitionistic Linear Logic

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 / transformations and formulas / proof terms. With linear implication representing ru...

Semantical Observations on the Embedding of Intuitionistic Logic into Intuitionistic Linear Logic

Intuitionistic Layered Graph Logic

Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic that gives an account of layering. As in bunched systems, the logic includes the usual intuitionistic connectives, together with a non-commutative, non-associative con...

Towards CERes in intuitionistic logic

Cut-elimination, introduced by Gentzen, plays an important role in automating the analysis of mathematical proofs. The removal of cuts corresponds to the elimination of intermediate statements (lemmas), resulting in an analytic proof. CERes is a method of cut-elimination by resolution that relies on global proof transformations, in contrast to reductive methods, which use local proof-rewriting ...

Towards Intuitionistic Dynamic Logic

We propose the beginnings of an intuitionistic propopsitional dynamic logic, and describe several serious open problems.