Agreement measures are useful tools to both compare different evaluations of the same diagnostic outcomes and validate new rating systems or devices. Cohen’s kappa (κ) certainly is the most popular agreement method between two raters, and proved its effectiveness in the last sixty years. In spite of that, this method suffers from some alleged issues, which have been highlighted since the 1970s; moreover, its value is strongly dependent on the prevalence of the disease in the considered sample. This work introduces a new agreement index, the informational agreement (IA), which seems to avoid some of Cohen’s kappa’s flaws, and separates the contribution of the prevalence from the nucleus of agreement. These goals are achieved by modelling the agreement—in both dichotomous and multivalue ordered-categorical cases—as the information shared between two raters through the virtual diagnostic channel connecting them: the more information exchanged between the raters, the higher their agreement. In order to test its fair behaviour and the effectiveness of the method, IA has been tested on some cases known to be problematic for κ, in the machine learning context and in a clinical scenario to compare ultrasound (US) and automated breast volume scanner (ABVS) in the setting of breast cancer imaging.

The Davis-Putnam-Robinson theorem showed that every partially computable $m$-ary function f(a₁, ..., a_m) = c on the natural numbers can be specified by means of an exponential Diophantine formula involving, along with parameters a₁, ... a_m, c, some number k of existentially quantified variables. Yuri Matiyasevich improved this theorem in two ways: on the one hand, he proved that the same goal can be achieved with no recourse to exponentiation and, thereby, he provided a negative answer to Hilbert's 10th problem; on the other hand, he showed how to construct an exponential Diophantine equation specifying f which, once a₁, ... a_m have been fixed, is solved by at most one tuple < v₀, ..., v_k > of values for the remaining variables. This latter property is called single-foldness. Whether there exists a single- (or, at worst, finite-) fold polynomial Diophantine representation of any partially computable function on the natural numbers is as yet an open problem. This work surveys relevant results on this subject and tries to draw a route towards a hoped-for positive answer to the finite-fold-ness issue.