PECR: A formal system based on computability logic

PECR is a formal system designed to explore the properties of computability of programs on a real-world computer. As such PECR incorporates the finite resources of the machine upon which a program is to be executed. The main features of the formal system will be presented and its practical applications will be discussed. Of particular interest is the implementation of the formal system to the exploration of the laws of nature that lead to rigorous constructions of computer models of real-world phenomena.