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            <idno type="halRefHtml">&lt;i&gt;32nd Annual German Conference on AI : Advances in Artificial Intelligence (KI 2009)&lt;/i&gt;, Sep 2009, Padernorn, Germany. pp.306-314, &lt;a target="_blank" href="https://dx.doi.org/10.1007/978-3-642-04617-9_39"&gt;&amp;#x27E8;10.1007/978-3-642-04617-9_39&amp;#x27E9;&lt;/a&gt;</idno>
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                <editor>Mertsching, Bärbel</editor>
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              <p>Analogy plays a very important role in human reasoning. In this paper, we study a restricted form of it based on analogical proportions, i.e. statements of the form ıt a is to b as c is to d. We first investigate the constitutive notions of analogy, and beside the analogical proportion highlights the existence of two noticeable companion relations: one that is just reversing the change from c to d w. r. t. the one from a to b, while the last one called ıt paralogical proportion expresses that ıt what a and b have in common, c and d have it also. Characteristic postulates are identified for the three types of relations allowing to provide set and Boolean logic interpretations in a natural way. Finally, the solving of proportion equations as a basis for inference is discussed, again emphasizing the differences between analogy, reverse-analogy, and paralogy, in particular in a three-valued setting, which is also briefly presented.</p>
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