<p>This article proposes a deductive justification for analogical arguments based on an intensional notion of possible equality. On the one hand, it introduces an inferential operational principle (DS), valid within a first-order intensional modal logic, which accounts for analogical inference. On the other hand, the strength of an analogical argument is explained in terms of modal attenuation: its conclusion is more or less possible depending on the number of possible worlds in which it holds true. The article argues that similarity can be understood as intensional equality and presents a formal semantics that explains its role in inference. Finally, it discusses how this proposal meets the logical criteria expected of a sound justification for analogical arguments.</p>