Distributive agents, illustrated

The following illustrates how deduction (backward-chaining) is performed.  Forward-chaining works very similarly.  I have left out how the agents find others to answer queries -- this is the routing strategy which is an optimization problem.

Agent2 performs only one step, namely, the resolution of:

• P\/Q (the query Agent2 is being asked)
  with
• ~P\/Q (the rule that Agent2 has in its KB)

This is another illustration, using a common-sense example:

By the way, the implication statement "A implies B":

     nice(X) ← sandals(X)

is classically equivalent to "not A or B":

     ~sandals(X) \/ nice(X)

and therefore it can be resolved with

    nice(matt)

by the substitution { X / matt }, yielding the resolvent:

    sandals(matt).

This is why the resolution step works.

Distributive architecture for inference engine (deduction)

Eureka!! This new architecture is much simpler:

Each agent responds to queries and spits out solutions. For example, if you believe that "professors who wear sandals are nice to students" then you listen to queries about "who is nice to students". When there is a hit, you either:

1. return an answer, if you know as a fact that XYZ is nice to students. 
2. return a sub-goal, in this case, "does XYZ wear sandals?" and wait for others to answer. 

In case #2, if you got an answer "Professor Matt Mahoney wears sandals", say with TV = 0.9, then you decide how to calculate the TV of the conclusion given that TV of premise = 0.9. The only calculation you need to perform is for the rule that you own. Then you return the answer to the asker.

This architecture is so wonderful because there is no need to construct the proof tree anymore. The proof tree seems to have disappeared but it is really implicitly constructed within the network of agents!

Thanks to Matt Mahoney for proposing the CMR (competitive message routing) architecture.

For reference, this is an older design that reveals my thinking:  (This can be seen as a single agent, building the proof tree internally while trying to answer 1 query.  In the new architecture each agent is responsible for applying only one rule at a time).

Self-programming architecture

This is not a new idea -- Ben and Jared in Opencog has mentioned it before (in the context of MOSES):

Abram seems to have an idea where the GP is replaced by RL (reinforcement learning).

Yesterday I was analyzing the GP + IE idea in more details:

1. Let the GP side and the IE side gradually evolve in cycles, starting with $GP_1 + IE_1$.
2. The key question is whether the cyclic route is faster than hand-coding IE.  Initially, it would involve more work because the GP side needs to be custom-made (we cannot use off-the-shelf GP software).  It may pay off only if $GP_1 + IE_1$ increases programming productivity significantly.
3. A very weak $IE_1$ cannot increase programming productivity because GP + weak IE is still too slow to be usable.  For example, one idea is to have IE suggest a number of primitive functions when given a goal, so GP can include those primitives in the genes for that population.  But, even with current state-of-the-art GP, this cannot efficiently solve > 1 line programs, even if primitives are suggested.
4. $IE_*$ (the ideal form of IE) will be able to deduce the program when given the desired goal: $$ G:goal \mapsto \{ P:program | \quad P \vdash G \}. $$ Whereas the above $IE_1$ is too weak (suggesting primitives similar to the goal): $$ G:goal \mapsto \{ x | \quad x \approx G \}. $$ Perhaps we need to find something in between weak $IE_1$ and $IE_*$.
5. In other words, we simply have to hand-code $IE_1$ to reach a certain level of functionality before putting it to use with GP.  That basic level seems to include:
• Ability to express simple plans (so that human teachers can supply basic programming knowledge as decomposition of tasks into sub-tasks)
• Ability to express similarity and to perform simple associative recall.
  
Interestingly, the ability to perform deduction seems not required for $IE_1$, nor the ability to calculate truth values.

The new insight may change our priorities during implementation...