Abstract
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.
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Notes
- 1.
In the following, we omit the universal quantifier for readability.
- 2.
- 3.
- 4.
All our datasets and python code used in this paper are freely available at https://github.com/arxaqapi/analogy-classifier.
- 5.
At this stage, we used PDTB version 2.1.
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Afantenos, S., Kunze, T., Lim, S., Prade, H., Richard, G. (2021). Analogies Between Sentences: Theoretical Aspects - Preliminary Experiments. In: Vejnarová, J., Wilson, N. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2021. Lecture Notes in Computer Science(), vol 12897. Springer, Cham. https://doi.org/10.1007/978-3-030-86772-0_1
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