Beyond Proportional Analogy

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 [...]

A Uniform Approach to Analogies, Synonyms, Antonyms, and Associations

In a previous post, I wondered how Latent Semantic Analysis (LSA) and Latent Relational Analysis (LRA) could be unified. LSA can be used to recognize synonyms and LRA can be used to recognize analogies. The two algorithms are quite similar, so it seems it should be possible to design a more general algorithm that [...]

The Logic of Attributional and Relational Similarity

In a previous post, I discussed the distinction between attributes and relations:
An attribute is a characteristic of an entity, whereas a relation is a connection between two or more entities. In logic, we can define an attribute as a predicate with one argument and a relation as a predicate with two or more arguments. The [...]