Charles Sanders Peirce Provable Categories

It was Charles Sanders Peirce, the great mathematician and philosopher, who first described the categories of description logic, long before any digital computers existed.

He proposed three universal categories, in a paper he’d entitled “On a New List of Categories” and presented to the American Academy of Arts and Sciences in 1877. He named these categories Firstness (Possibility), Secondness (Actuality), and Thirdness (Necessity). This concept of categories and their relationships has broad application. For example, the scientific method is a derivative from these categories.

These categories are often shown as a triangular graph where each is dependent upon the other two. When applied to Information Technology, logical data models show Possibility, databases maintain Actuality, and message & logic flows are a Necessity.

These categories and their dependencies define a description logic-based AI structure that is mathematically and technically specific.

  • Possibility: These are the logical models that only allow consistent updates to Actuality.
  • Actuality: These are all existing facts that are created and updated. Changes to logical model facts are applied to Possibilities and changes to flow facts are applied to Necessity.
  • Necessity: The logical flow and data flows that apply updates to Actuality. The Update and Consistent flows with Possibility are not direct; they occur when the facts of Possibility are updated in Actuality.

Provable logical descriptions of each of these categories is accomplished by AI with specific reasoners:

The semantic reasoner verifies the consistency of the logical relationships defined in the logical model. The axiomatic reasoner verifies that all facts are possible within the logical model. The path reasoner uncovers contradictions in logic and data flows.

The mathematically sound structure of Peirce’s Categories guarantees logical consistency.  Consistency is when an entire system adheres to semantic, axiomatic, and path reasoning in all category components as defined in computer languages.

All information is persisted as facts, including the Model and the Path Flow. Since all facts of Peirce categories must be consistent within the logical model, the synchronization of the categories must therefore be consistent.

The synchronization of the categories by people requires human intelligence assisted by reasoners to update and create content. Artificial Intelligence is when computer systems update and create content within the logical model and, when necessary, provide synchronization by resolving contradictions.

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