Wednesday, January 1, 2014

2013 year in review

This last year has had a considerably transformative effect on me. After seeing the considerable usefulness of orders to partitioning and decomposing entities into parts and places I decided to switch my primary focus to order theory. I made partial orders the core of my computer algebra system and I begun to explore the concepts of order theory in more detail.

By examining the ways in which enumerations could be combined I also stumbled upon ordinal numbers. I then realized that the number system should not be limited to finite numbers and instead it should be extended to include transfinite numbers like the ordinals. From there I stumbled upon the surreal numbers and transseries and I have been working on implementing them ever since.

My interest in order theory led me to consider the different classes of partial orders such as antichains, total orders, weak orders, interval orders, and series parallel orders and the fact that these are themselves ordered by inclusion. This led me to build an ontology of my own and to consider other ontologies that other people have constructed such as Dolce, Cyc, SUMO, and GFO.

Through my examination of these different ontologies I begun to consider fundamental questions of how an ontology should be constructed. One of my conclusions which is encouraged by the results of causal set theory is that the ontology of concrete entities should be an ontology of processes and events which may be related to one another causally.

After this I begun to consider how my reasoning engine and ontology could be extended to deal with more general AI applications. It is my conclusion that my logical core should be extended with modules to dealing with uncertainties such as procedural uncertainty and declarative uncertainty. The core of my AI framework should then be a combined ontology and module system.

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