Research Notes - Analogy comparison

[dnorman]

Following research notes #1

The goal is to perform symbolic inference over analogies recorded within the system.
Presently, associative analogies are the focus, though this also applies to other forms of analogies, like Catagorical analogies. More on that later.

Those associative analogies essentially contain two Symbols, corresponding to left and right. Each of these two Symbols is not one identifier, but rather a set containing potentially many Members. Members reference ClaimIDs made previously within the Mindbase system.

For a given Associative Analogy, There is no pairwise association between the Member in these two sets – Only a single association between the two sets as a whole. It has been clear for some time that fuzzy sets / fuzzy logic would be necessary as part of the mindbase system.

One way to think about this fuzzyness is in terms of confidence of "sameness" or "correctness" but this is problematic, insofar as it assumes that there exists some god's-eye, or approximation thereof which can be used to adjudicate relative sameness in an absolute sense. This perspective is fraught with problems.

One of the core ideas of this project is that all things which can be observed within the universe are similar (at least pairwise) along some axes, and dissimilar along others. Whether those dimensions are spatial or ontological; whether observed from the world, or made from whole cloth (noting that even fictions are observations first.)

With this in mind, another way to think about fuzzyness is in terms of metric proximity in some dimension within an abstract metric space.

A Symbol for Hygge is proximate to a Symbol for Cozy within this metric space, but they are not the same. We must derive this proximity through measurement of analogies and anti-analogies between those symbols, but also by omission, presumably in the form of a relative-strength analysis with other symbols.

For instance, There may be some categorical analogies made between the English Symbols for Caliente and Picante, but those should necessarily be fewer and/or weaker than those between Hot and Scalding.

The outcome of yesterday's experimentation (#1) strongly implies that this scoring isn't just something which happens at query time. Indeed, such symbols are constructed as the product of queries, but are themselves used construct new Analogies. As such, the partial matching of one side of the associative Analogy should result in ALL of the Members from the other side being retained for their bound symbol variables, albeit with a lesser score than if the opposing side were a perfect match.

Some questions which follow from this:

• How should this score be calculated within a single candidate Analogy?
  • This scoring can't just be from Left to Right. We have to do the inverse as well. How does bidirectional scoring work?
  • How do we reconcile left-side matching=right-side-scoring with right-side matching = left-side-scoring? Hypothesis: Narrowing of the set of Members is done by same-side matching. Scoring of the remaining Members is done by opposite-side matching.
• How should we compose the bound symbol variable Members across multiple Analogies which are under consideration?
  • What about identical ClaimIDs which originate from different Analogies with different scores?
  • Should these be averaged, or otherwise be combined via some weighted sigmoid function?

[KevinWMatthews]

Did Atom get deleted from the the Glossary, or maybe you plan to add it later? I can't seem to find it at the moment, though I do have a fair idea of what it means.

Tiny note - is Calliente a Spanish word? If so, I thought that it only has one L - two would change the pronunciation, right?

[dnorman]

@KevinWMatthews Apologies for the delay in responding. Atom was renamed to Member in the glossary. I have corrected the error here. I have also corrected the spelling of caliente ;)