For some time now, I’ve been experimenting with algorithms for solving proportional analogies. A proportional analogy has the form A:B::C:D, meaning “A is to B as C is to D“. For example, quart:volume::mile:distance means “quart is to volume as mile is to distance”. Multiple-choice proportional analogy problems were part of the SAT college entrance test until 2005, and they are still part of the GRE and MAT tests. It seems that proportional analogies capture an important aspect of cognition, but it also seems that they are a bit simplistic, when compared to the kinds of analogies that we use in the real world. For example, consider the analogy between the solar system and the Rutherford-Bohr model of the atom. We could express the analogy as sun:planet::nucleus:electron, but this proportional analogy is overly simplified. Recently I was able to extend my previous work on proportional analogies to include more complex analogies.
Latent Relational Analysis (LRA) measures the relational similarity between pairs of words, such as quart:volume and mile:distance. LRA is able to solve proportional analogy questions from the SAT, such as the following:
The idea behind LRA is to characterize the relation of a pair (e.g., quart:volume) by searching in a very large collection of text for all phrases that contain the pair (e.g., “a volume of three quarts”). The relation is represented by a vector of frequencies of contextual patterns.
The Latent Relation Mapping Engine (LRME) extends LRA to larger systems of relations, such as the following:
The idea behind LRME is to measure the quality of a mapping from a source domain (e.g., the solar system) to a target domain (e.g., the Rutherford-Bohr model of the atom) by the sum of relational similarity measures for all of the proportional analogies that it implies (e.g., sun:planet::nucleus:electron, sun:mass::nucleus:charge, planet:revolves::electron:revolves, etc.). This simple idea works surprisingly well. On a set of twenty mapping problems, ten from science analogies and ten from common metaphors, it achieves human-level performance.
Filed under: Computational Linguistics, Semantics | Tagged: analogy, metaphor, relations, similarity
Kia ora Peter
It is interesting you should analyse the metaphor-analogy ’syndrome’ this way. I have often discussed the distinction between the analogy and the metaphor with educated colleagues to find, to my astonishment, that most cannot clearly define a distinction between the two. I put it down to the lack of occurrence of having to really think about it.
When discussing the matters with colleagues in the blogosphere I found that there existed there a far clearer vision of the differences, probably because the participants had actually put some time into thinking about the differences.
Thanks for this analysis of analogy.
Best wishes
from Middle-earth
So now you are getting closer to what Bertrand Russell called the relation number:
“A relation number is defined as the class of relations consisting of all those relations that are similar to one member of the class.”
And you might begin to see why Russell said of their relevance to empiricism:
“I think relation-arithmetic important, not only as an interesting generalization, but because it supplies a symbolic technique required for dealing with structure. It has seemed to me that those who are not familiar with mathematical logic find great difficulty in understanding what is meant by ’structure’, and, owing to this difficulty, are apt to go astray in attempting to understand the empirical world. For this reason, if for no other, I am sorry that the theory of relation-arithmetic has been largely unnoticed.”
It is interesting you should analyse the metaphor-analogy ’syndrome’ this way.
Here are two excellent papers about the relation between metaphor and analogy:
Bowdle, B., & Gentner, D. (2005). The career of metaphor. Psychological Review, 112(1), 193-216.
Gentner, D., Bowdle, B., Wolff, P., & Boronat, C. (2001). Metaphor is like analogy. In D. Gentner, K. J. Holyoak, & B. N. Kokinov (Eds.), The analogical mind: Perspectives from cognitive science (pp. 199-253). Cambridge, MA: MIT Press.
And you might begin to see why Russell said of their relevance to empiricism:
It’s interesting that your second link is to a bibliography on structural realism. Russell supported structural realism until his views were criticized by MHA Newman. Newman’s criticism is easily avoided by ontic structural realism.
It isn’t clear to me that “Russell’s later epistemology”, as referred to by Solomon, is distinguishable from ontic structural realism. However, it does appear that there may be some fundamental difficulty with the very concept of mathematical structure that has yet to be ferreted out as indicated to by Solomon’s observation that “In Russelian structure, the domain of a system of relations consists only of the fields of the relations, and these fields need not be sets.”
In any case, part of the reason I’m so concerned with relation arithmetic, per se, is that appears to me likely to provide structural realism with the symbolic power necessary to unify levels of thought more effectively than most other approaches.
After reviewing your linked web page on Ontic Structural Realism, it is becoming more urgent that I convince the scholars in this area to take more seriously Quine’s monumental feat of clearing away semantic underbrush with his description of relata as syntactic sugars for relations.
I really think a lot more progress could be made if scholars would state their arguments in terms of Quine’s syntax.
This reminded me of the semantic differential which I studied back in college. Though in the case of SD the source wasn’t a large text base, but sample space of test subjects.
I only mention it because I intuit there may be some overlap between these tools.
This reminded me of the semantic differential which I studied back in college. Though in the case of SD the source wasn’t a large text base, but sample space of test subjects.
Yes, Osgood’s semantic differential is related. See my work on sentiment and semantic orientation, especially measuring praise and criticism, which explicitly discusses Osgood. You might say that the basic idea of a lot of my work is to avoid bothering human test subjects (or knowledge engineers), by extracting equivalent information from a large body of text.
Mr Turney:, I congratulate you for your work, It is great. I discovered your work today, I am working in opinion mining.
I am definitely going to read more of your stuff.
I was thinking about a relatively new field in natural language processing called textual entaliment: http://nlp.stanford.edu/pubs/rte2-report.pdf
you can define this subarea of nlp as: The textual entailment problem is to determine if a
given text entails a given hypothesis.
Which include the determination if one text can be infered from another. This could be used for proportional analogies, and also opinion mining corpus, that will help you with the proportion of agreement and disagreement, but it would give you information only regarding that (agree or not)
Best regards