  We discuss a novel framework for physical theories that is based on the
principles of locality and operationalism. It generalizes and unifies previous
frameworks, including the standard formulation of quantum theory, the convex
operational framework and Segal's approach to quantum field theory. It is
capable of encoding both classical and quantum (field) theories, implements
spacetime locality in a manifest way and contains the complete modern notion of
measurement in the quantum case. Its mathematical content can be condensed into
a set of axioms that are similar to those of Atiyah and Segal. This is
supplemented by two basic rules for extracting probabilities or expectation
values for measurement processes. The framework, called the positive formalism,
is derived in three completely different ways. One derivation is from first
principles, one starts with classical field theory and one with quantum field
theory. The latter derivation arose previously in the programme of the general
boundary formulation of quantum theory. As in the convex operational framework,
the difference between classical and quantum theories essentially arises from
certain partially ordered vector spaces being either lattices or anti-lattices.
If we add the ad hoc ingredient of imposing anti-lattice structures, the
derivation from first principles may be seen as a reconstruction of quantum
theory. Among other things, the positive formalism suggests a statistical
approach to classical field theories with dynamical metric, provides a common
ground for quantum information theory and quantum field theory, introduces a
notion of local measurement into quantum field theory, and suggests a new
perspective on quantum gravity by removing the incompatibility with general
relativistic principles.
