Reasoning and Logic

Attributes and Relations: Redder than Red

Posted on January 5, 2007 by Peter Turney

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 distinction between attributes and relations can be unclear. For example, the colour red may be seen as an attribute, RED(X), or a relation, REDDER_THAN(X, Y).

I am slowly coming to believe that (1) the distinction between attributes and relations is fundamental to many different fields, (2) attributes are typically considered primary in some sense, whereas relations are secondary, yet (3) it is actually relations that are primary and attributes that are secondary. In fact, I suspect that attributes are simply a convenient fiction.

In the field of physics, these three points are the core of Lee Smolin’s The Life of the Cosmos. Smolin associates attribute-based physics with Newton and relation-based physics with Leibniz. He makes a persuasive argument that the Newtonian paradigm has dominated physics, but it is fundamentally flawed, and it is slowly being replaced with the Leibnizian paradigm.

In the field of cognitive psychology, Dedre Gentner has spent her academic life studying the psychology of attributes and relations. She has found that attributes tend to be learned earlier, but relations tend to gain importance as the individual matures. Our most sophisticated thinking is analogical reasoning, which is based on recognizing similarities in relations.

In the field of machine learning, entities are usually represented as feature vectors; that is, vectors of attributes. Inductive Logic Programming allows machine learning with relational representations, but ILP is less popular than feature-based learning. Probabilistic reasoning also favours attribute-based representations, although researchers are working on relational representations for probabilistic models.

In the field of philosophy of mind, qualia are used to argue against materialist treatments of consciousness. The experience of seeing the colour red is the traditional example of a quale. The Inverted Spectrum argument seems to show that there is something fundamental to the experience of redness, which cannot be reduced to the firing of neurons. But David Cole makes a strong argument that the Inverted Spectrum argument contradicts empirical observation. In essence, Cole argues that red is not actually an attribute; it is really a relation.

In the field of computational linguistics (my own field, if I must be pinned down), much research has gone into the problem of measuring the similarity between two words. This is a form of attributional similarity. More recently, research has addressed the problem of measuring relational similarity between pairs of words. Although there is a longer history behind attributional similarity measures, it may be that relational similarity measures are more important for computational linguistics. Experiments seem to show that relational similarity cannot be reduced to attributional similarity, but I suspect that it may be possible to reduce attributional similarity to relational similarity, and I have started sketching an algorithm for performing this reduction.