Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Analogical proportions, i.e., statements of the form a is to b as c is to d, state that the way a and b possibly differ is the same as c and d differ. Thus, it expresses an equality (between differences). However expressing inequalities may be also of interest for stating, for instance, that the difference between a and b is smaller than the one between c and d. The logical modeling of analogical proportions, both in the Boolean case and in the multiple-valued case, has been developed in the last past years. This short paper provides a preliminary investigation of the logical modeling of so-called “analogical inequalities”, which are introduced here, in relation with analogical proportions.

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