Automated generation and analysis of logical statements.

摘要

Propositional logic has applications in several areas including computer science, engineering, mathematics, proof complexity, and philosophy. One of the benefits of propositional logic is that there is a procedure for determining the validity of statements using truth tables. However, there is a need to develop more efficient methods for analyzing statements. A set of logical connectives developed by C.S. Peirce can be used as an alternative to notations of symbolic logic. These connectives provide at least three advantages. First, using the connectives, logical statements are amendable to statistical analysis based on symmetry groups. Second, new rules can be formulated that can be used to identify tautologies. These rules can be used as the basis for deduction. Third, the connectives can be used to visualize the structure of logical statements and the application of rules in deductions.