A possible worlds semantics for trustworthy non-deterministic computations

The notion of trustworthiness, central to many fields of human inquiry, has recently attracted the attention of various researchers in logic, computer science, and artificial intelligence (AI). Both conceptual and formal approaches for modeling trustworthiness as a (desirable) property of AI systems are emerging in the literature. To develop logics fit for this aim means to analyze both the non-deterministic aspect of AI systems and to offer a formalization of the intended meaning of their trustworthiness. In this work we take a semantic perspective on representing such processes, and provide a measure on possible worlds for evaluating them as trustworthy. In particular, we intend trustworthiness as the correspondence within acceptable limits between a model in which the theoretical probability of a process to produce a given output is expressed and a model in which the frequency of showing such output as established during a relevant number of tests is measured. From a technical perspective, we show that our semantics characterizes the probabilistic typed natural deduction calculus introduced in D'Asaro and Primiero (2021)[12] and further extended in D'Asaro et al. (2023) [13]. This contribution connects those results on trustworthy probabilistic processes with the mainstream method in modal logic, thereby facilitating the understanding of this field of research for a larger audience of logicians, as well as setting the stage for an epistemic logic appropriate to the task.