Logical Basis of Dimensionality

Modeling Semantic Cognition as Logical Dimensionality Reduction

Semantic knowledge is often expressed in the form of intuitive theories, which organize, predict and explain our observations of the world. How are these powerful knowledge structures represented and acquired? We present a framework, logical dimensionality reduction, that treats theories as compressive probabilistic models, attempting to express observed data as a sample from the logical conseq...

The Logical Basis of Metaphysics

The logical basis of phylogenetic taxonomy.

Phylogenetic taxonomy, like modern Linnean taxonomy, was modeled on a phylogenetic tree rather than a cladogram and, like its predecessor, perpetuates the use of morphology as a means of recognizing clades. Both practices have generated confusion in graphical representation, operational terminology, and definitional rationale in phylogenetic taxonomy, the history of which is traced. The followi...

Dimensionality reduction based on an overcomplete basis

We discuss a strategy of sparse approximation that is based on the use of an overcomplete basis, and evaluate its performance when a random matrix is used as this basis. A small combination of basis vectors is chosen from a given overcomplete basis, according to a given compression rate, such that they compactly represent the target data with as small a distortion as possible. As a selection me...

Decision implication canonical basis: a logical perspective

Article history: Received 11 October 2011 Received in revised form 19 March 2014 Accepted 16 May 2014 Available online 11 June 2014