Structure Mapping Engine - Structural Evaluation Score

Structural Evaluation Score

Once the match hypotheses are generated, SME needs to compute an evaluation score for each hypothesis. SME does so by using a set of intern match rules to calculate positive and negative evidence for each match. Multiple amounts of evidence are correlated using Dempster’s rule resulting in positive and negative belief values between 0 and 1. The match rules assign different values for matches involving functions and relations. These values are programmable, however, and some default values that can be used to enforce the systematicity principle are described in .

These rules are:

1. If the source and target are not functions and have the same order, the match gets +0.3 evidence. If the orders are within 1 of each other, the match gets +0.2 evidence and -0.05 evidence.
2. If the source and target have the same functor, the match gets 0.2 evidence if the source is a function and 0.5 if the source is a relation.
3. If the arguments match, the match gets +0.4 evidence. The arguments might match if all the pairs of arguments between the source and target are entities, if the arguments have the same functors, or it is never the case that the target is an entity but the source is not.
4. If the predicate type matches, but the elements in the predicate do not match, then the match gets -0.8 evidence.
5. If the source and target expressions are part of a matching higher-order match, add 0.8 of the evidence for the higher-order match.

In the example match between p1 and p2, SME gives the match between the transmit relations a positive evidence value of 0.7900, and the others get values of 0.6320. The transmit relation receives the evidence value of 0.7900 because it gains evidence from rules 1, 3, and 2. The other matches get a value of 0.6320 because 0.8 of the evidence from the transmit is propagated to these matches because of rule 5.

For predicates p3 and p4, SME assigns less evidence because the arguments of the transmit relations are functions. The transmit relation gets positive evidence of 0.65 because rule 3 no longer adds evidence. The match between (input gear) and (switch circuit) becomes 0.7120. This match gets 0.4 evidence because of rule 3, and 0.52 evidence propagated from the transmit relation because of rule 5.

When the predicates in p3 and p4 are attributes, rule 4 adds -0.8 evidence to the transmit match because — though the functors of the transmit relation match — the arguments do not have the potential to match and the arguments are not functions.

To summarize, the intern match rules compute a structural evaluation score for each match hypothesis. These rules enforce the systematicity principle. Rule 5 provides trickle-down evidence in order to strengthen matches that are involved in higher-order relations. Rules 1, 3. and 4 add or subtract support for relations that could have matching arguments. Rule 2 adds support for the cases when the functors match. thereby adding support for matches that emphasize relationships.

The rules also enforce the difference between attributes, functions, and relations. For example, they have checks which give less evidence for functions than relations. Attributes are not specifically dealt with by the intern match rules, but SME’s filter rules ensure that they will only be considered for these rules if they are part of a higher-order relation, and rule 2 ensures that attributes will only match if they have identical functors.