Sunday, February 23, 2014

Logical organization of declarative knowledge

Mathematical logic provides the foundation for the organization of all declarative knowledge stored by an intelligent agent. By creating an ontology we can organize our knowledge base in terms of the logical classification of entities. The main categories in a logical ontology of mathematical entities are ordered collections, unordered collections, algebraic structures, and elements of algebraic structures. Relations are specified as unordered collections of ordered collections and algebraic structures are specified as a system of relations over a underlying set.

Well Von Neumann ordinals can be specified as unordered collections numbers including naturals, integers, rationals, reals, surreals, complex numbers, numbers, surcomplex numbers, quaternions, octonions, among others can be specified as elements of algebraic structures. In this way the four categories of the upper ontology described previously are sufficiently powerful to classify most mathematical entities.

The only limitation of this approach to classification is that partially observable systems cannot be described as mathematical structures in the traditional sense. Nonetheless, it is my contention that we can represent the set of states a partially observable system may take and reason about them using logic. We can enrich the system with a mereology and then form a logical ontology of parts of the system.

Well it is certainly true that logic provides an ideal foundation for the formalization of all declarative knowledge this doesn't mean that we don't need more then this for general intelligence such as a system of procedural knowledge for approximate optimization, a module system for loading domain specific knowledge such as interaction, and an advanced learning system for acquiring new knowledge and transforming modules.

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