Artificial General Intelligence

Inference Rules

1. Revision

The revision rule combines distinct bodies of evidence for the same statements.

Compared to Dempster's rule of combination: there are different interpretations of "evidence combination". In NARS, it is a form of average, while in D-S theory, it is a form of conjunction.

NAL tolerates inconsistency in knowledge, though it is different from the existing paraconsistent logic and belief revision.

2. Choice

The choice rule chooses among competing answers to a question.

For an evaluative question, the statement with a higher confidence value is preferred; for a selective question, the statement with a higher expectation value is preferred.

Given two competing answers, one with a confirmation record of 19 out of 20, and the other n out of n, when we should prefer the latter when n gets larger? It depends on the value of k.

3. Forward inference

A syllogistic rule requires the two premises to share one term, and produces a conclusion between the other two terms.

For the inheritance copula, the two premises have four possible combinations, and only one of them corresponds to a valid rule in IL-1. In NAL-1, all can be valid when associated with a proper truth-value function.

Truth-value functions are determined according to the semantics, by treating the involved measurements as extended Boolean variable.

A variant of syllogistic rule is a rule for immediate inference, which only takes one premise.

An inference rule of NAL can be either "strong" or "weak", depending on whether it converges to an inference rule in IL. This distinction is similar to the traditional distinction between "deductive" and "inductive" inference, or between "explicative" and "ampliative" inference.

4. Backward inference

A question and a judgment can be used as premises to derive another question, iff the answer of the derived question and the judgment can be used as premises to derive an answer to the original question.

5. Relations among the rules

The syllogistic rules of NAL-1 are reversible, in the sense that to exchange a conclusion and a premise leads to another rule.

Because of the reversibility of the rules, the rule tables for forward and backward inference are the same, except truth-values.

The conclusion of any rule can be used as a premise of any other rule. To avoid circular inference, the two premises must have distinct bases. Example:

⟨a --> b⟩.
⟨b --> c⟩.
⟨a --> c⟩.

Credit-assignment problem.

In NAL: If a conclusion is revised, usually both premises will be revised, too. Example:

  IN: ⟨a --> b⟩. %1.00;0.60% {0 : 1} 
  IN: ⟨b --> c⟩. %1.00;0.30% {0 : 2} 
  IN: ⟨a --> c⟩. %0.00;0.80% {0 : 3} 
100
  IN: ⟨a --> b⟩?  {100 : 4} 
  IN: ⟨b --> c⟩?  {100 : 5} 
  IN: ⟨a --> c⟩?  {100 : 6} 
1
 OUT: ⟨a --> b⟩. %1.00;0.60% {0 : 1} 
 OUT: ⟨a --> b⟩. %0.86;0.64% {58 : 3;1;2} 
 OUT: ⟨b --> c⟩. %1.00;0.30% {0 : 2} 
 OUT: ⟨b --> c⟩. %0.47;0.48% {13 : 3;2;1} 
 OUT: ⟨a --> c⟩. %0.00;0.80% {0 : 3} 
 OUT: ⟨a --> c⟩. %0.05;0.81% {2 : 2;3;1}

Reading