Analogies between sentences: Theoretical aspects -preliminary experiments

Overview & Synopsis

Analogical proportions hold between 4 items a, b, c, d insofar as we can consider that "a is to b as c is to d". Such proportions are supposed to obey postulates, from which one can derive Boolean or numerical models that relate vector-based representations of items making a proportion. One basic postulate is the preservation of the proportion by permuting the central elements b and c. However this postulate becomes debatable in many cases when items are words or sentences. This paper proposes a weaker set of postulates based on internal reversal, from which new Boolean and numerical models are derived. The new system of postulates is used to extend a finite set of examples in a machine learning perspective. By embedding a whole sentence into a real-valued vector space, we tested the potential of these weaker postulates for classifying analogical sentences into valid and non-valid proportions. It is advocated that identifying analogical proportions between sentences may be of interest especially for checking discourse coherence, question-answering, argumentation and computational creativity. The proposed theoretical setting backed with promising preliminary experimental results also suggests the possibility of crossing a real-valued embedding with an ontology-based representation of words. This hybrid approach might provide some insights to automatically extract analogical proportions in natural language corpora.