Recap of progress

For those following the latest news you will have learned that tremendous progress has been taking place in the Tauchain community. Below I will recap some of the highlights of that progress:

• Github Update: Dragan adds support for equality and inequality.
• Support for integers being worked on.
• Proof extraction implemented (mostly).
• Conjunctive Query Containment implemented (mostly).
• Preliminary optimizations based on Conjunctive Query Containment being worked on.

And this is just the summary of TML updates. There is also work being done on the alpha discussion platform (2 developers working on it), the whitepaper is nearly done,  and more. 

What are our thoughts worth?

This particular question has been asked before on Steem. @sushie asked this question. 

But to ask this question in the context of Tauchain is a bit different. We know for example that Steem has a mechanism of price discovery where by Proof of Brain it has been shown that collaborative filtering produces price discovery. The price of a piece of content is determined in accordance to the amount of upvotes it gets as a percentage of the reward pool. This is not the same thing as the actual worth of the content which could be worth a lot more but it does tell us how much a particular piece of content is worth on Steem.

On Tauchain there will be a knowledge market and there will be a means of determining how much bits of knowledge is worth. On Tauchain knowledge can be useful to knowledge bases which are like databases designed specifically to house knowledge on different subjects. To go into some particulars on the technical aspects of Tauchain there is an important concept called "satisfiability". To define this concept which to be particular is "Boolean Satisfiability" I will first state that just as in programming or in logic Boolean implies that there are a binary answer to the problem.

In other words if I ask a question and by definition it is a question which can only by answered with true or false (1 or 0) then we have what is known as a Boolean satisfiability problem. This is a particular kind of problem which TML is designed to solve efficiently. In fact, conjunctive query containment is an optimization which can help with constraint satisfaction, which is a very particular kind of problem which Wikipedia defines below:

Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of intense research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. The Boolean satisfiability problem (SAT), the satisfiability modulo theories (SMT) and answer set programming (ASP) can be roughly thought of as certain forms of the constraint satisfaction problem.

The nature of these particular kinds of problems known as CSPs are that they require combinatorial search as the method of solving them. We know for example Sudoku solvers work by applying a depth first search through the search space. The possible combinations of Sudoku are known and there is supposed to be only one solution. As you can see this is quite useful and a very common problem category to be solved.  

For TML Ohad implemented conjunctive query containment which for prescient readers provides a hint leading directly to the paper titled: "Conjunctive-Query Containment and Constraint Satisfaction" which in it's text states that conjunctive query containment and constraint satisfaction are the same problem (just different names).   

For another example of this kind of problem take a look at a Rubik's cube and note that every cube has a finite amount of possible positions that it can be in, with the goal position and the starting position, with the user of the Rubik's cube seeking to get from the starting position to the goal position as quickly (efficiently) as possible. A Rubik's cube can easily be solved by Tauchain TML if you can define it in TML and if TML has the ability to act as a SAT Solver.

All of this is cool technical speak but how does it relate to how Tauchain might determine how much bits of knowledge is worth? Well if it's required to solve a particular problem how much is solving that problem worth? If the problem is worth a lot to be solved then the knowledge required to solve it would become quite highly sought after. I cannot personally predict what kind of problems Tauchain will be able to solve but I'd guess it would be better than toy problems like the Sudoku puzzle. That said, just as you can decentralize solving the Sudoku puzzle by distributing the required computation (either human computation or machines), you can apply this same kind of decentralization to do more interesting stuff like proving theorems or doing advanced mathematics. 

References

1. Kolaitis, P. G., & Vardi, M. Y. (2000). Conjunctive-query containment and constraint satisfaction. Journal of Computer and System Sciences, 61(2), 302-332.

2. Chen, J. (2011). Solving Rubik's Cube Using SAT Solvers. arXiv preprint arXiv:1105.1436.

3. https://en.wikipedia.org/wiki/Constraint_satisfaction_problem

4. https://steemit.com/motivation/@sushie/how-much-is-your-thought-worth

5. https://github.com/IDNI/TML/commits/master