A Survey of E-Test Spaces

Abstract

Test spaces (or quasimanuals) were introduced byD. Foulis and C. Randall in 1972 as a language fordescribing the empirical sciences. They emphasized thattest spaces give a direct description of laboratory operations. Information is lost in moving froma test space to its corresponding logic, and for thisreason, test spaces provide a more fundamentaldescription of a physical system. Recently, A.Dvurecenskij and S. Pulmannova have introduced ageneralization of test spaces, called D-test spaces, inorder to include a description of unsharp measurements.In the present work, we consider an equivalent framework called an effect test space or E-test space forshort. This gives an alternative viewpoint that isbelieved to be simpler and more natural. Moreover, theproofs of results are more direct. This framework also has connections with some of the recentwork of D. Foulis, R. Greechie, M. K. Bennett, and G.Ruttimann.