Separating the basic logics of the basic recurrences

TL;DR

This paper demonstrates that different types of recurrences in Computability Logic validate distinct principles, highlighting fundamental logical differences between parallel, countable, and uncountable branching recurrences.

Contribution

It reveals that basic recurrences in Computability Logic have inherently different logical validations, clarifying their fundamental logical distinctions.

Findings

Parallel recurrences validate certain principles.

Countable branching recurrences validate different principles.

Uncountable branching recurrences validate yet another set of principles.

Abstract

This paper shows that, even at the most basic level, the parallel, countable branching and uncountable branching recurrences of Computability Logic (see http://www.cis.upenn.edu/~giorgi/cl.html) validate different principles.