Calculating self-referential statements,I: Explicit calculations |
| |
Authors: | Craig Smorynski |
| |
Affiliation: | (1) Westmont, Illinois |
| |
Abstract: | The proof of the Second Incompleteness Theorem consists essentially of proving the uniqueness and explicit definability of the sentence asserting its own unprovability. This turns out to be a rather general phenomenon: Every instance of self-reference describable in the modal logic of the standard proof predicate obeys a similar uniqueness and explicit definability law. The efficient determination of the explicit definitions of formulae satisfying a given instance of self-reference reduces to a simple algebraic problem-that of solving the corresponding fixed-point equation in the modal logic. We survey techniques for the efficient calculation of such fixed-points. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|