Spring 2009 Semester

It has been a wile since a new post. But, I have been attentive to school; and since the break is over once again, back to school again.

During this break I did not get much work completed. I played Tetris for hours, which, may be considered work, but not constructive work. On my arrival to Erie, I continued to play Tetris on my Dreamcast; and then would spend 20 min to 1 hour a day working. This is not enough time and focus to get much work done. But I again read sections from a discrete and combinatorical mathematics handbook; this strenghted my views on the topic. And, thus far, I have developed the following.

* The continued basis containing the axioms
* A translation from predicate statements to the propositional logic
* The generation of combinatorial space oracles in deterministic bounded time
* And, the relationship between the $\forall x \in L P(x) \rightarrow \bigwedge_{x\in L}^n \exists P(x)$. This allows for the predicate $\forall$ to be removed from the basis and replaced with the existential predicate as a propositional form. The notation $P(x)$ can be removed, and is done with the operation of independent negation from the previous axiom definitions. This is omitted for clarity.

The final bullet can be applied as the combinatorial space itself, or more likely a subset of the combinatorical space as a constraint on the system.

Much still needs to be done in the formalization of this system but must be set aside for the sake of the current semester.