Grounding Meaning: Composition versus Abstraction

I recently read an interesting paper, How Is Meaning Grounded in Dictionary Definitions? The abstract follows:
Meaning cannot be based on dictionary definitions all the way down: at some point the circularity of definitions must be broken in some way, by grounding the meanings of certain words in sensorimotor categories learned from experience or shaped by [...]

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 [...]

Brownian Motion — Why It Is Important

Bloggers are making poetry out of the search terms that lead people to their blogs. I had to try it myself.
Each line below, including the title, is a query that led a visitor to my blog. I adjusted the capitalization of the queries and added punctuation.
Don’t worry, I won’t quit my day job.
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Language Affects Perception

Here’s an update to my post on the Sapir-Whorf Hypothesis. Lera Boroditsky answered the question, “What have you changed your mind about?” as follows:
I used to think that languages and cultures shape the ways we think. I suspected they shaped the ways we reason and interpret information. But I didn’t think languages could shape [...]

Three Levels of Thought

Peter Gärdenfors proposes that there are three levels of abstraction for modeling thought:

Symbolic: logic, expert systems, Prolog, Cyc, good old-fashioned AI, theorem proving
Spatial: geometry, feature spaces, conceptual spaces, semantic spaces, information retrieval, vector space models, latent semantic analysis, machine learning
Connectionist: neural networks, Hebbian theory, associationism, perceptrons, neuroscience

These levels might be compared to modeling physics at [...]

Readings in Analogy-Making

Here are some links to interesting books, papers, people, and websites related to analogy-making and metaphor. If I’m missing a link that you would recommend, please leave a comment. Look here for a list of quotations about analogy-making and metaphor. There is no particular order to these lists.
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Code for Big Tensors

I recently completed a technical report on tensor decomposition, Empirical Evaluation of Four Tensor Decomposition Algorithms. The tech report has two messages: (1) If you like Singular Value Decomposition, you’re going to love Tucker Decomposition. (2) Many interesting applications involve large tensors. If your application requires large tensors, the tech report includes MATLAB source code [...]

Tensors for Data and Text Analysis

For the last several months, I’ve been playing with tensors as an approach to data and text analysis. Here are some pointers to get started on tensors.
Tensors are a generalization of matrices to higher dimensions:

order 0 tensor = scalar
order 1 tensor = vector
order 2 tensor = matrix
order n > 2 tensor = higher order tensor

PARAFAC [...]

Analogy, Ethics, Cooperation, Evolution, and the Golden Ratio

Consider an analogy of the form A:B::C:D, “A is to B as C is to D”; for example, “mason is to stone as carpenter is to wood”. This kind of analogy is often called a proportional analogy. The Greeks believed that proportional analogy is like the numerical equation A/B = C/D; for example, 1/2 = [...]

The Symbol Grounding Problem

There is a view that the meaning of words (more generally, of symbols) must be grounded in sensory perception or in physical interaction with the world (embodiment). If symbols were merely defined in terms of other symbols, then it seems that we would have an infinite regression; we would spin in circles in symbol space, [...]