Multiple-valued extensions of analogical proportions.

Abstract

This paper provides a discussion of different multiple-valued extensions of logical expressions of analogical proportions that are equivalent in the Boolean case. It is advocated that these extensions may serve different goals, or at least reflect different views. Boolean expressions of analogical proportions, modeling statements of the form A is to B as C is to D, are first restated and commented. An approach to handling the case of binary attributes that may not apply in the Boolean setting is also outlined via a proper encoding.