A Bigraph Relational Model

In this paper, we present a model based on relations for bigraphical reactive systems [Milner09]. Its defining characteristics are that validity and reaction relations are captured as traces in a multi-set rewriting system. The relational model is derived from Milner's graphical definition and directly amenable to implementation.Comment: In Proceedings LFMTP 2011, arXiv:1110.668

Linear contextual modal type theory

When one develops, implements, and studies type theories based on linear logic, for example, in the context of theorem proving, logic programming, and formal reasoning, one is immediately confronted with questions about their equational theory and how to deal with logic variables. In this paper, we propose linear contextual modal type theory that gives a mathematical account of the nature of logic variables. Our type theory is conservative over intuitionistic contextual modal type theory proposed by Nanevski, Pfenning, and Pientka. As a technical contribution we provide a proof of soundness, and, as a justification for its usefulness, we shed some light on the difficulties working with logic variables in linear logics that contain ⊤.