Re: Peirce List Discussion • HP

A computational problem is defined as a set of problem instances with specified properties.  An algorithm solves a problem if it computes the correct answer to every problem instance in that set.

The use of a problem instance as an expository example is to represent its problem class and to provide some idea of how the algorithm works.  A single problem instance can always be addressed by special pleading but the test of an algorithm is whether it handles the whole set of problem instances.

The program I wrote uses an extended topological variant of Peirce’s Alpha Graphs as its main data structure for representing propositions and it uses a general purpose algorithm that finds the complete set of satisfying logical interpretations for any proposition given on input.  This is tantamount to using propositional calculus as a very simple form of declarative programming language.

References

• Theme One Program • User Guide
• Applications of a Propositional Calculator • Constraint Satisfaction Problems