Mathematical system of potential infinities (II) – formal systems of logical basis

This is the second part of the effort to resolve the following two problems that badly need an answer: how can an appropriate theoretical foundation be chosen for modern mathematics and computer science? And, under what interpretations can modern mathematics and the theory of computer science be kept as completely as possible?

The paper sets out the foundation for the system.

Here, the logical foundation for the mathematical system of potential infinities is given.

The logical calculus, which will be used as the tool of deduction in the PIMS, is established. This new tool of reasoning is a modification of the classical two‐value logical calculus system.