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Last updated 10/02/2016

PREDICATE INVENTION

Empirical axiomatic theories: empirical contents of data.

Empirical axiomatic theory definition

Representation of data types in empirical axiomatic theories

The first step of the analysis of empirical content of data consists of the representation of data in empirical axiomatic theories. Below we consider several known data types such as comparisons, binary matrices, matrices of orderings, matrices of proximity and attribute-based matrix. Moreover, empirical axiomatic theories are the most general representation of various data types. They represent well known data types, mixture of various data types, and data types that have no numerical representation at all.

Next, we review existing methods for processing these data types. This includes determination of assumptions of existing methods. Finally, we show that Relational methods such as MMDR do not require restrictive assumptions about data types. Any data type can be accommodated and even discovered in training data. It is known that humans answer more precisely for qualitative and comparative questions than for quantitative questions. Therefore, the representation of these data types in axiomatic empirical theories is convenient.

  • Attribute-based matrix
  • Matrix representation of binary Relations
  • Matrices of orderings
  • Matrices of closeness