Analogy-making is at the core of human intelligence and creativity with applications to such diverse tasks as commonsense reasoning, learning, language acquisition, and story telling. This paper studies analogical proportions between booleans of the form `$a$ is to $b$ what $c$ is to $d$' called boolean proportions. Technically, we instantiate an abstract algebraic framework of analogical proportions -- recently introduced by the author -- in the boolean domain consisting of the truth values true and false together with boolean functions. It turns out that our notion of boolean proportions has appealing mathematical properties and that it coincides with a prominent model of boolean proportions in the general case. In a broader sense, this paper is a further step towards a theory of analogical reasoning and learning systems with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity.

Analogical proportions are statements of the form "A is to B as C is to D" that are used for several reasoning and classification tasks in artificial intelligence and natural language processing (NLP). For instance, there are analogy based approaches to semantics as well as to morphology. In fact, symbolic approaches were developed to solve or to detect analogies between character strings, e.g., the axiomatic approach as well as that based on Kolmogorov complexity. In this paper, we propose a deep learning approach to detect morphological analogies, for instance, with reinflexion or conjugation. We present empirical results that show that our framework is competitive with the above-mentioned state of the art symbolic approaches. We also explore empirically its transferability capacity across languages, which highlights interesting similarities between them.