Abstract. Analogical proportions are statements involving four entities, of the form ‘A is to B as C is to D’. They play an important role in analogical reasoning. Their formalization has received much attention from different researchers in the last decade, in particular in a propositional logic setting. Analogical proportions have also been algebraically defined in terms of factorization, as a generalization of geometric numerical proportions (that equate ratios). In this paper, we define and study analogical proportions in the general setting of lattices, and more particularly of distributive lattices. The decomposition of analogical proportions in canonical proportions is discussed in details, as well as the resolution of analogical proportion equations, which plays a crucial role in reasoning. The case of Boolean lattices, which reflects the logical modeling, and the case corresponding to entities described in terms of gradual properties, are especially considered for illustration purposes.

Language software applications encounter new words, e.g., acronyms, technical terminology, loan words, names or compounds of such words. To add new words to a lexicon, we need to indicate their base form and inflectional paradigm. In this article, we evaluate a combination of corpus-based and lexicon-based methods for assigning the base form and inflectional paradigm to new words in Finnish, Swedish and English finite-state transducer lexicons. The methods have been implemented with the open-source Helsinki Finite-State Technology (Lindén & al., 2009). As an entry generator often produces numerous suggestions, it is important that the best suggestions be among the first few, otherwise it may become more efficient to create the entries by hand. By combining the probabilities calculated from corpus data and from lexical data, we get a more precise combined model. The combined method has 77-81 % precision and 89-97 % recall, i.e. the first correctly generated entry is on the average found as the first or second candidate for the test languages. A further study demonstrated that a native speaker could revise suggestions from the entry generator at a speed of 300-400 entries per hour.

information in distributive lattices