To steal a dog; to kidnap a dog, especially by force or deception.
From dog + nap (from kidnap, which comes from Dutch 'kappen' to grab). The term is a modern coinage (mid-1900s) formed by analogy with kidnap, showing how English creates new words by analogy with existing patterns.
Dognap is a perfect example of word-creation through analogy—once we had 'kidnap' (person-napping), English speakers naturally created 'dognap' (dog-napping) following the exact same pattern!
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