Explicit mathematics was introduced by Feferman around 1975. The original aim of explicit mathematics was to provide a natural formal framework for Bishop-style constructive mathematics. Soon it turned out, however, that the range of applications of explicit mathematics is much wider and includes several subjects.
Following the tradition of classical proof theory, we are interested in the proof-theoretic analysis of
systems of second order arithmetic and set theory. Special emphasis is presently put on the following
three topics: theories of (iterated) admissible sets and beyond, metapredicative systems and
lifting the proof theory of second order arithmetic to theories of sets and classes.
The problem of data privacy is to verify that confidential information stored in an information system is not provided to unauthorized users and, therefore, personal and other sensitive data remain private. The main challenge in such a context is to share some data while protecting other personally identifiable information.
Modal logic is the study of reasoning that involves various modalities.
It goes as far back as Aristotle, although the modern treatment of modal
logic is usually attributed to C. I. Lewis's work at the beginning of 20th
century, and encompasses diverse subareas.