Grounding Operators: Transitivity and Trees, Logicality and Balance

We formally investigate immediate and mediate grounding operators from an inferential perspective. We discuss the differences in behaviour displayed by several grounding operators and consider a general distinction between grounding and logical operators. Without fixing a particular notion of grounding or grounding relation, we present inferential rules that define, once a base grounding calculus has been fixed, three grounding operators: an operator for immediate grounding, one for mediate grounding (corresponding to the transitive closure of the immediate grounding one) and a grounding tree operator, which enables us to internalise chains of immediate grounding claims without loosing any information about them. We then present an in-depth proof-theoretical study of the introduced rules by focusing, in particular, on the question whether grounding operators can be considered as logical operators and whether balanced rules for grounding operators can be defined

Checking Trustworthiness of Probabilistic Computations in a Typed Natural Deduction System

In this paper we present the probabilistic typed natural deduction calculus TPTND, designed to reason about and derive trustworthiness properties of probabilistic computational processes, like those underlying current AI applications. Derivability in TPTND is interpreted as the process of extracting $n$ samples of possibly complex outputs with a certain frequency from a given categorical distribution. We formalize trust for such outputs as a form of hypothesis testing on the distance between such frequency and the intended probability. The main advantage of the calculus is to render such notion of trustworthiness checkable. We present a computational semantics for the terms over which we reason and then the semantics of TPTND, where logical operators as well as a Trust operator are defined through introduction and elimination rules. We illustrate structural and metatheoretical properties, with particular focus on the ability to establish under which term evolutions and logical rules applications the notion of trustworhtiness can be preserved

BRIOxAlkemy: A Bias detecting tool

We present a tool for the detection of biased behaviours in AI systems. Using a specific probability-based algorithm, we provide the means to compare the action of the user’s algorithm of choice on a specific feature that they deem “sensible” with respect to fixed classes and to a known optimal behaviour

THE COMPLEX INTERPLAY BETWEEN VITAMIN D DEFICIENCY AND DIABETES

It has been recently highlighted the link between vitamin D and metabolic and immunological pro- cesses, which established its role as an essential component of human health preservation. Vitamin D has been defined as natural immune modulators, and through the activation of its receptors (VDRs), it regulates calcium metabolism, cellular growth, proliferation and apoptosis, and other immunological functions. In this setting, vita- min D has also been reported to influence glucose regulation via effects on insulin secretion and action. Vitamin D deficiency is strongly associated with obesity mostly due to the storage of vitamin D in adipose tissue because of its lipophilic properties. The decrease in vitamin D levels may occur through several mechanisms such as a decrease in the calcium concentration, an increase in PTH, or a direct effect of vitamin D on worsening insulin resistance and secretion, augmenting the risk of developing type 2 diabetes. On the other hand, retrospective analysis and observational studies demonstrated high prevalence of vitamin D deficiency in patients with type 1 diabetes and suggested a contributory role in the pathogenesis of type 1 diabetes, specially with certain allelic variations of the VDR. Vitamin D supplementation during pregnancy and early childhood decreased the risk of autoimmune dia- betes and perhaps, even after the onset of diabetes, it may improve glycemic control. In addition, in subjects that are affected by a high risk of developing diabetes (impaired fasting glucose and/or glucose tolerance, possibly without obesity) vitamin D supplementation could be helpful on the prevention of type 2 diabete